Expert: Bobby Soltani - 6/27/2005

Question
Tom and Cathy decide to run a race. Tom can run at 10 meters per second and Cathy can run at 6 meters per second. Tom gives Cathy a 50 meter head start. How long is it before Tom catches Cathy?

I'm having troble transfering this into an equation. Perhaps you could help?

Distressed, Jeremy

Answer
Hi Jeremy,

Let Tom start at 0 meters.  Then, the distance he has traveled as a function of time is
d = 10t
where d is the distance and t is the time in seconds.  For example, after 3 seconds, he has traveled 30 meters.

Since Cathy got a head start, she will start at 50 meters.  So, the distance she has traveled is
d = 6t + 50
We want to know when Tom catches her so we need to set the equations to equal each other.

10t = 6t + 50
subtract 6t from both sides
4t = 50
t = 12.5

So, after 12.5 seconds, Tom and Cathy will have both traveled 125 meters.

Let me know if you have any questions.

Bobby