Another interesting math puzzle...?

Question

Three cyclists go out for the day. Two are on a tandem and one on an ordinary bicycle. Disaster struck when the ordinary bicyle was stolen while they were having lunch. They were left with the tandem and 20 miles to go. The tandem has to have two riders and the third person walks. Mary can walk a mile in 20 minutes, Ben in 30 minutes and George in 40 minutes. The tandem travels at 20 miles per hour no matter which pair is riding it. What is the shortest time for all three to get home?

Any answers, and any explanations?

Have fun... 10 points for the clearest explanation with answer.

Answer 1

Is it as straight forward as it appears??

If Mary does the walking, she will walk 20 miles in 400 minutes = 6 hours & 40 minutes.

Thats how much it wil take the other two to ride the tandem. Thus they will all reach in the same time. That must be the shortest time.

Do I earn the 10 points????

Answer 2

mary walks at first while the other 2 use the bicycle. In 1 hour when the other two arrive at their destinations, mary will be 17 miles from her destination. One person on the bicycle goes back for mary and makes it to her in 1 hour and 20 minutes. with 13 miles to go. both mary and the other person ride the bike back in 39 minutes. Add it all up and all three make it back in 2 hours and 59 minutes

Answer 3

it'l take 1 hour for the tandem to reach the destination. im thinking that mary should walk as she can walk the fastest. even then.. the shortest time for all three to get home will be 20 mins x 20 miles= 400 min. which = 6 hrs 35 min approx

Answer 4

6 hours 40min. Mary walks and the other two ride home on the tandem. Of course they could drive back and pick her up or something.

Answer 5

M(ary)=3mph
B(en)=2mph
G(eorge)=1.5mph
T(andem)=20mph

divide the distance by thirteen.
20/13 miles (approximately 1.538miles)

|-| = 1/13 of total distance.(1.538 miles)
(tandem1)
|-|-|-|-|-|-|-|-|-|-|-|-|-|
|--------B----|--G--|

(tandem2)
|-|-|-|-|-|-|-|-|-|-|-|-|-|
|----G---|-----M----|

(walk)
|-|-|-|-|-|-|-|-|-|-|-|-|-|
|---M----|-G-|--B--|


every cut in the tandem means, they leave the tandem behind and walk. so when george rides the tandem after 9.231miles (6*20/13), he leaves the tandem behind, and mary rides it after she walks for 9.231 miles. this way, they'll all get home within 3.846hours.

Person=(rate)*segments walked*(20/13)+(tandem's rate*segments on tandem)*(20/13)=time before the person got home.


M=(1/3)*6*(20/13)+(1/20)*7*(20/13)=3.615hours
B=(1/2)*4*(20/13)+(1/20)*9*(20/13)=3.769hours
G=(2/3)*3*(20/13)+(1/20)*10*(20/13)=3.846hours


and this way, they all walk for the same amount of time.^_^

Answer 6

I think there is a better way that they can use.

Ben & geroge get on the tandem and cycle to home, while mary walks lonely, (It may she see the thief in the way). After an hour Ben and george get to home. At this time mary was walked 3 miles from the restaurant and 17 miles remained to home. Then one of them rides lonely to get to the mary. The speed of the lone rider is 10 miles per hour. (notice that the speed of a lone rider is 10 miles per hour because no pair was different. This means all were same in riding)

If we name the velocity of Mary as V(M) and velocity of Lone rider as V(L) then by answering this equation the time the rider took to get to the mary founds.

V(M) = 3 miles per hour
V(L) = 10 miles per hour

V(M)t + V(L)t = 17
=> 3t + 10t = 17
=> 13t = 17
=> t ~1.3 hour (~ 80 min)

=> distance mary walked after 80 min (after first 3 miles walking) is (1.3)*3=3.9 miles.

OK mary walked 3 miles and then 3.9 miles (altogether equals to 6.9 miles) and then Lone rider get to her (13.1 miles remained to home).

Lone rider asks mary "What hapended? Did you see anything? Did you go to the police office?" and mary responds "NO, I should get to home as soon as possible, because this is a puzzle"

No mary gets on the tandem and both riding to home the distance of 13.1 miles with avarage speed of 20 miles per hour. I saw the mary was to tired after a long walk and decided to let the remaind distance 14 miles with 20 miles per hour speed (In fact I want to let her cycle slowly, Because she is really tired).

OK how long does it take 14 miles with the speed of 20 miles per hour? That's right 0.7 hour or 42 mins.

after 1 + 1.3 + 0.7 hours (altogether approximately 3 hours) they all get to home. Or sooner.

Very nice puzzle.

Thanks.
Be Succeed.