# uniform motion problem: A car started out from Memphis towar

#### Gretchen Vivanco

##### New member
I need help with a uniform motion problem!

A car started out from Memphis toward Little Rock at a rate of 60 km/h. A second car left from the same point 2 hours later and drove along the same route at 75 km/h. How long did it take the second car to overtake the first car?

I know that rate * time = distance

so I have the rate of each, but I just don't really know where to go from there???

#### Mrspi

##### Senior Member
Re: uniform motion problem

Gretchen Vivanco said:
I need help with a uniform motion problem!

A car started out from Memphis toward Little Rock at a rate of 60 km/h. A second car left from the same point 2 hours later and drove along the same route at 75 km/h. How long did it take the second car to overtake the first car?

I know that rate * time = distance

so I have the rate of each, but I just don't really know where to go from there???
Let t = number of hours traveled by first car

The rate for the first car is 60 km/hr, so
distance for first car = 60*t

The second car left 2 hours later, so it will travel 2 hours LESS. The time traveled by the second car is t - 2 hours.

The rate for the second car is 75 km/hr, so
distance for second car = 75(t - 2)

When the second car catches up with the first car, they will have traveled the same distance, right?

distance for first car = distance for second car
60t = 75(t - 2)

Ok...now you can take over. Remember, you are asked to find out how long it takes the second car to overtake the first car, so your answer will be the time for the SECOND car.

I hope this helps you.

#### Gretchen Vivanco

##### New member
thank you!

Thank you so much for your help!!! I understand now!!