Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Two runners are running for $1$ hour in the Olympic stadium.

One of them $A$ is faster than the other one $B$.

Runner $A$ completes $50$ rounds in $1$ hour and runner $B$ completes $35$ rounds in $1$ hour.

The runners are switching between them a torch while $A$ is holding the torch at the beginning.

Every time $A$ passes $B$ they are switching the torch between them.

How many rounds the torch completed the stadium in $1$ hour?

I tried to build equations but didn't succeed.

Thank you.

share|improve this question

1 Answer 1

up vote 2 down vote accepted

Main question:

How much time has past between start and the first join of $A$ and $B$?

Let's say after $t$ hours.

After $t$ hours $50t$ rounds are done by $A$ and $35t$ rounds by $B$. So $50t=35t+1$ and $t=\frac{1}{15}$. Then after $\frac{2}{15}$ hours they join for the second time. The torch was for $\frac{1}{15}$ hours in the hands of $A$ and for $\frac{1}{15}$ hours in the hands of $B$ so there were $50\times\frac{1}{15}+35\times\frac{1}{15}=\frac{85}{15}=\frac{17}{3}$ rounds for the torch in $\frac{2}{15}$ hours. That gives $\frac{7\times17}{3}$ rounds in $\frac{7\times 2}{15}=\frac{14}{15}$ hours. Then they join for the $14$-time and the torch now goes to $A$. That results in $50\times\frac{1}{15}=\frac{10}{3}$ rounds for the torch in the last $\frac{1}{15}$ hours and we end up with $\frac{7\times17}{3}+\frac{10}{3}=43$ rounds in $1$ hour.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.