- #1

brotherbobby

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- Homework Statement
- 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 ##v_1 = 5\,\text{km/h}## and the other rode off on the bicycle at a speed of ##v_2 = 15\,\text{km/h}##. The tourists agreed to leave the bicycle at intermediate points between which one walks and the other rides.

(1) What will the mean speed of the tourists be?

(2) How long will the bicycle remain unused?

- Relevant Equations
- For uniform motion with velocity ##v_0## along a straight line where ##x(t=0)=x_0## and the motion starts at ##t=0##, the position of the object at any time ##t## is ##x=x_0+v_0t##.

**Problem :**I copy and paste the problem as it appeared in the text.

**Attempt :**##\texttt{I could make no significant attempt at solving the problem.}##

The only thing I realise is that if the two tourists be A and B, A travels on the bicycle for a while, leaves the bicycle and walks. B catches up with the bicycle and overtakes A who is on foot and stops at a distance further, leaving the bicycle and continues to walk. A catches up with the bicycle and cycles on. This continues till they both reach the camp at the same time.

However, every trial I made (manually), A and B don't arrive at the camp at the same time.

Or going backwards, taking arrival at the camp to be simultaneous, when I trace back, giving them times on and off the bicycle, they don't start off together.

##\texttt{How to decide how much time they spend on foot and how much time on the bicycle?}##

**Request :**Any help or hint would be welcome.