Solve the PCT puzzle…

(Inspired by Reno Dave – don’t you wish you paid more attention during algebra class?)

PCT Puzzle:

Hiker A starts walking north from Sierra City, mile 1197.6, on Saturday 13 July, averaging 25 miles a day with 1 day off each week.

Hiker B starts walking south from the Canadian border, mile 2660.0, on Monday 15 July, averaging 30 miles a day with 0.5 days off each week.

At what mile and on what day will the two hikers meet?

For bonus points, what is the closest trail town to that mile?

You must show all workings of how you reached your answer.

The first correct response will receive a pair of Dirty Girl Gaiters provided by the one and only Dirty Girl, Xy!

Responses will be assessed on a peer judgement basis, as my trail brain already malfunctions calculating distances between water sources!

If maths ain’t your thang, feel free to take a guess at where UB and I will cross paths on the trail!


30 thoughts on “Solve the PCT puzzle…

  1. Show Your Work!?!! How do I do that on this little comment Pad!! This take trig and calculus! OK Fine, give me 5 minutes…..

  2. You will pass on a day so bright that the reflection of your souls will be so overwhelming that you must do nothing else but pass each other. Xo
    (Failed Maths many of times)

  3. There are advantages to being stuck in an ankle brace, loving word problems, and the PCT … I hope!

    My guess is that they’ll meet on Tuesday, August 13 at mile 1812 with UB hiking 798 miles and MukMuk hiking 614 miles.

    Closest trail town will Crater Lake Mazama Village at mile 1829.

    Show my work !?!

    If UB is doing 30s with a nero day once a week, his actual average mileage is 27.857 miles per day. / If MukMuk is doing 25s with a zero once a week, her actual average is 21.428 miles per day.

    Together they can knock out 49.284 miles per day. They need to close a distance of 1462 miles. MukMuk will be doing 50 miles before UB starts, so actual distance to close is 1412 miles. They will meet in 29.649 days.

  4. In a 7 day week, muk will average 21.43 miles/day and will travel 2 days while UB stays put. On the morning of the 15th, she will be at or about mile 1,240.6. They will be separated by 1,419.54 miles. UB will be averaging 27.86 mpd in a 7 day week. Collectively, they will be on a collision course at 49.28 mpd. Therefore, 1,419.54 miles divided by 49.28 mpd equals 28.8 days. They should enjoy an awesome reunion on August 12 at mile 1,857.

    Thanks for sharing your journey!!!

  5. Hiker A starts from Sierra City heading north from mile 1197.6 on Saturday July 13 and averages 150 miles in 7 days because of 1 rest day. This means in 4 weeks on Aug. 10, Hiker A reaches mile 1797.6. Add on 2 more days of hiking after that and Hiker A reaches mile 1847.6 on August 12.

    Hiker B begins hiking southbound from the Canadian border at mile 2660.0 on Monday July 15 and averages 30 miles a day with .5 rest day a week. I take that means he only hikes 15 miles that day and 30 the other 6 days, so he averages 195 in 7 days. In 4 weeks time Hiker B reaches mile 1880.0 on August 12.

    This means that on Tuesday August 13, the paths of Hiker A and Hiker B will cross at one point during the day. Probably in the afternoon. I can’t find out what city is near this point but I believe it is in Crater Lake National Park.

  6. No No Your all wrong PCT Angel! They will cross at Mile 1890! With UB doing 770 and Muck doing 692. :p But yea Crater Lake will be the closet major point around there. πŸ™‚ Or it Muk Muk kick’s it a little they could meet at Shelter Cove Resort. Al;though I have no idea what is there.

    1912 Shelter Cove Resort
    1884 Windigo Pass
    1852 Hwy 138
    1840 Crater Lake N

    Two trains, rather slow trains, are approaching each other one is traveling 30 miles a day for 92.85% of the week and the other train is traveling at 25 miles per day for 85.71% of the week. When these two trains collide the world will be a better place, at least for a day or two! πŸ˜€

    6.5/7=95.85%*30=27.855 Miles per day
    6/7=85.71%*25=21.4275 Miles per day
    2660 – 1198 – 100 = 1362 /(27.855+21.4275)=27.64 Days until the Collision
    27…. * 27.5 = 770 Miles for UB
    21…. * 27.5 = 692 Miles for Muk Muk (added back in the 100 miles)

    I can Draw pictures too!

    God, I really should do some work today, Na, it’s just a mess off day!!

    PS: Where’s Chris, good job, I forgot about the 100 miles, but I think you forgot to add it back in. πŸ˜€

  7. Ok, here it goes……………I WANT MY DIRTY GIRL GATORS!
    On 7/15 Muk Muk will be at mile 1247.60
    On 7/15 UBserios will be at mile 2660.00
    add 150 miles a week for MUK and 195 a week for UBS
    week 1
    on 7/22 MUK will be @ mile 1397.60
    UBS will be @ mile 2465.00
    week 2
    on 7/29 MUK will be @ mile 1547.60
    UBS wil be @ mile 2270.00
    week 3
    on 8/05 MUK will be @ mile 1697.60
    UBS will be @ mile 2075.00
    week 4
    on 8/12 MUK will be @ mile 1847.60
    UBS will be @ mile 1880.00
    on 8/13 MUK will be @ mile 1872.60
    8/13 UBS will be @ mile 1850.00
    1872.60 – 1850.00 = 22.60 is the mileage difference between the two, divide by 2 = 11.30

    Tuesday August 13, 2013
    both of you will meet @ mile marker 1861.30 Thielsen Creek Trail (found on halfmile
    I hope Chemult Oregon is the closest town (found on
    DO I WIN????

  8. If MukMuk hikes 25 miles six days in a row starting Jul 13 and then takes a zero, and if she repeats that pattern, on Aug 11 she will be at mile 1847.6 (having had a zero on Aug 9). If UB hikes 30 miles six days in a row starting Jul 15 and hikes 15 miles on the seventh day, and if he repeats that pattern, Aug 11 will be a 15 mile day and end at mile 1880, 32.4 miles north of MukMuk.

    If they start at the same time on Aug 12 and if UB’s miles per hour pace is 30/25 times MukMuk’s, they will meet at 25/55*32.4 = 14.7 miles from where MukMuk starts = Mile 1862.3. However, since in a previous blog MukMuk said UB hikes faster for less time and she hikes slower for more time, UB’s mph pace is probably greater than 30/25th MukMuk’s, and they will meet slightly south of that mile.

    HOWEVER, if they are really 87.4 miles apart at the start of Aug 11, I suspect they will both put in max days and end up together late in the evening of Aug 11!

    But, per Wolfman’s note, I suspect UB will have put it in a slightly high gear the previous week and they’ll meet at Crater Lake on Aug 11.

  9. Now that I’m on my second iced coffee for the afternoon … YIKES … I’m gonna stick with my guess Wolfman.

    It’s all in the wording. It’s only 50 miles you account for given her stated start date and location and she states that UB is starting at 2660 (monument) not 2669 (Manning Park).

  10. Rozi simple:

    You are travelling at 25 miles 6 out of 7 days so on average 25 * 6/7 = 21.43 miles/day

    On the 2 days head start you moved 42.86 miles

    He is travelling 30 miles 6.5 out of 7 days so on average 30 * 6.5/7 = 27.86 miles/day

    Assuming you meet at equal time and Distance = Time x Speed

    Distance 1 = 21 .43 x T
    Distance 2 = 27.85 x T

    D1/D2 = 21.42/27.85

    D1 + D2 = Total Distance

    Total Distance = 2660 – 1197.6 – 42.86 Miles (head start)

    D2 = 1419.54-D1

    D1 = 0.77 * (1419.54 – D1)

    D1 = 1093.05-.77D1

    1.77D1 = 1093.05

    D1 = 617.54 miles

    D2 = 1419.54-617.54 = 802 miles

    Meeting Location = 617.54 + 42.86 + 1197.6 = Mile 1858

    Time = 617.54/21.43 = 28.81 Days after the 15/07 (because I’ve already accounted for the head start

    Time = 12/08/2013 @ 7:26 PM @ Mile 1858

    • Nice Chris! Now can you do the graphical representation that goes along with this? X + Y = Z or some such fun!

      Great Fun Muk Muk, but regardless it’s a month to when you all join back up. Maybe a day or two either way depending on where and how you to stop it out on the last week or so. I think this is the most fun I have had doing math in a long time. πŸ˜€

  11. Hi Rozi by my calculations you will meet UB on the 16th August. Bon Chance. By then you will definitely have a new niece or nephew.

  12. I agree Wolfman, the best fun I’ve had in a really long time. Now that the caffeine has worn off … I can see I indeed needed to add in the additional miles for MukMuk, actual intercept will be mile 1858 as noted by Chris Beckman. Or perhaps 1857 as Scott states if you don’t use the third decimal point. I’m still sticking with Tuesday, August 13.

  13. I LOVE this! More algebra than we’ve seen since school! This reminds me of my high school backpacking days, when my dad and his hiking buddy, both with PHDs in chemistry, debated for a couple of hours if you could theoretically dehydrate alcohol.

    Back to the hiking problem. I think you’ve missed a variable: as you get to the last week before meeting, both of you will probably be adding speed to make it quicker to see each other. Time for me to resharpen the pencil…

  14. Some of you are relying on math alone (let’s call that an IQ approach) while I am factoring in some human factors (let’s call that an EQ approach). THEREFORE, unless they miss each other entirely because at the very moment UB reaches MukMuk on the trail, she is in fact a few feet off-trail in the shrubbery taking her morning constitutional, I predict the following:

    Place: Mile 1861.4, Thielsen Creek.
    Date: August 12 Time: 11:00am.

    This takes into account the following factors:
    1. MukMuk will start even earlier than usual on Aug. 12 because she will be very focused on the day’s mission. Thus, she will have hiked a greater percentage of her day’s miles by 11am than UB. She will do better than 10 by 10 that day.

    2. Also, Halfmile notes both a SB and NB Water Alert relating to mile 1861, so both parties will be highly motivated to get to mile 1861, and will spend some time there getting water. So they may not arrive at 1861.4 at exactly the same time, but whichever one arrives later will find the other still there, getting water and taking a rest (or, as MukMuk would say, a “sit down” or a “lie down.”)

    Caveat: Since Chemult is the closest town in the vicinity, Hiker A and Hiker B could collaborate to change their respective hike pace to meet there, since apparently a foot-high sandwich is available there:

    So, if Hiker A and Hiker B meet on August 12 at Mile 1861, OR if they are seen eating a sandwich like the one depicted in the link above on August 12, then by all rights, I win the DirtyGirl gaiters.

    • Jamie, I like the way you think! I have the same mileage as you but a day later.
      However, I really want the Dirty Girl Gaiters. I wrote Gators, the first time, my daughter will be one come August!

      • Brooke, when you receive the baby alligator that MukMuk has already mailed you (in a Priority Mail box with holes punched in the sides), perhaps you’ll learn to be more careful in your typing! I hope you win the Gaiters, but I fear that Chris will win with all that flashy-looking formula stuff he/she posted — it looks like the blackboard in Good Will Hunting!

      • Jamie, I like your witty sense of humor. I’m famous for typo’s and creating my own words and changing song lyrics. I back pedaled and my daughter really is going to be a Gator.
        Gators scare me, but I think MukMuk’s Gaiters are amazing and I would use them. On a practical note, I hope one of us wins!
        I am Rozanne’s greatest fan! Our hiking group HTHC (Holy Thursday Hiking club) has started a fan club. We will be taking care of MukMuk when she arrives in Washington!
        We Love Our Girl!

  15. I’ll be keeping it in my brother’s pool til August and then I’ll be sending it off, to my daughters apartment, at the U of F. Do you have any great names for this Gator before my daughter releases it into the wild? I’m thinking WTF (welcome to Florida). I can hear it now………….”Mother what were you thinking?”
    I’m thinking we need a post from Muk Muk, right about now.

  16. Ok, I gave the puzzle to my niece to solve. She came up with the happy reunion at mile 1861.4 on 8/13. You can find her solution at:

    I’d like to introduce a bit of human element, and since I don’t have a current mileage map, I’m going to say they will meet at Windigo Pass at 10am on Tuesday, August 13th!

    This was quite a fun riddle and gave me quite an opportunity to educate my niece about thru hiking . . . she now wants to meet you too when I kidnap you!

  17. Two wondering souls, with their own individual goals, some with sore toes, shall reunite amongst towering pines, stream-side, to sharing their joy & dreams, regardless of the miles journeyed, buoyed with anticipation, but content to forge on enjoying the trail.
    (but I ain’t got no proof of this!).

  18. Hi darling, I like to challenge the match and started to figure it out but could not find the right calculations. Instead of numbing my brains I gave them a rest and did not find out the answer. Love Mutti xxoo

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