Two tourists who are at a distance of 40 km from their camp must reach it together in the shortest possible time . they have one bicycle which they decide to use in turn. One of them started walking at a speed of 5km/hr and the other rode off on the bicycle at a speed of v2=15 km/hr . the tourists agreed to leave the bicycle at intermediate points between which one walks and the other rides . what will the mean speed of the tourists be ? how long will the bicycle remain unused.?

Question

Two tourists who are at a distance of 40 km from their camp must reach it together  in the shortest possible time . they have one bicycle which they decide to use in turn. One of them started walking at a speed of 5km/hr and the other rode off on the bicycle at a speed of  v2=15 km/hr . the tourists agreed to leave the bicycle at intermediate points between which one walks and the other rides . what will the mean speed of the tourists be ? how long will the bicycle remain unused.?

experimentx · Answer

two people one bicycle, one rides while other walks, and after sometime the rider stops and waits for the walking one ...and the walking one rides and the riding one walks ... this cycle continues.  Is this the question is saying?

anonymous · Answer

uhmm...when the cycler stops , it leaves the cycle and w/o waiting starts to walk..i think so

experimentx · Answer

Oo ... so. looks like i misinterpreted the question.

anonymous · Answer

hmm..its a tough one. can take a lot of time :/

anonymous · Answer

i think that  when the cyclist has covered 5km he should get off....then walk..... similarly...every 5km they should get off.....maybe

anonymous · Answer

with hit and trial ....I got that after 10 km he should get off.....not 5km...

but I need a proper ans

anonymous · Answer

Ans.  minimum possible time = 5 hrs 20 min
Avg speed= 7.5 km/hr 
and time when the bike was unused = @hrs 40 min

anonymous · Answer

* bike is unused for 2 hrs 40 minutes

diyaja · Answer

can u please explain you solution?

diyaja · Answer

your*

anonymous · Answer

I don't know the solution ....:/ I just know the answers

diyaja · Answer

oh.. then lets just keep working on it

anonymous · Answer

yup.

experimentx · Answer

when the distance is symmetric, it works ... d=20 km/ time=20/5 + 20/15.

diyaja · Answer

if the distance is symmetric the one who rides the cycle first should wait for the other person after covering that particular distance.. right?

experimentx · Answer

solving this will give the answer http://www.wolframalpha.com/input/?i=d%2F5+%2B+%2840-d%29%2F15+%3D+d%2F15+%2B+%2840-d%29%2F5 however still not so plausible.

experimentx · Answer

it assumes that when the time taken by one tourist = time taken by another tourist, time is minimum. from there we get the distance at which first tourist leaves the bike and another picks it up. and we can solve for the rest.

diyaja · Answer

i get it, ty!