Question

A bus has traveled 210 miles, and continues at a rate of 50 miles per hour. A van has driven 170 miles, and continues at a rate of 60 miles per hour. In how many hours will the two vehicles have traveled the same distance?

Answer 1

Lets look at the bus first. Lets say i asked you to give me how far the bus traveled in one hour, what would you do?

Answer 2

It travels 50 miles in one hour according to the question

Answer 3

would i set it up d+rt(bus)=d+rt(van)?

Answer 4

But it has already traveled 210 miles, so we must add that to this case. Now, all we would need to do is create a fancy equation that would set us up to answer this when asked to find out how far it's traveled for ANY time.

Do you have an idea on how to do that?

Answer 5

Yup, that's exactly how you would need to set it up!

Answer 6

so would it be 210+50t=170+60t and solve for t?

Answer 7

where d = distance already traveled, r = speed and t = time(unknown). We set them equal to each other since we want to know when they would be equal distances at time 't'.

Yup yup!

Answer 8

so t would equal 4?

Answer 9

yup