Finding the rate of speed

Question

Two cars leave Indianapolis, one traveling east and the other west. After 3 hours, they are 297 miles apart. If one car is traveling 5 mph faster then the other, what is the speed of each?

Answer 1

Hi Desiree,

Thanks for posting the question!

So, I approached this as if I was solving a distance problem (of course, here you have 2 distances). I hope the steps I show you make sense.

Let:
S = speed of the slower car
S + 5 = speed of the faster car


The 297 represents the distance between them. And that distance can be found using the calculations of the individual distances traveled by each car, and adding those values together.

Time:
3 (hours)

Distance traveled in 3 hours (Slow car):
3 times S = 3S

Distance traveled in 3 hours (Fast car):
3 times (S + 5) = 3S + 15

Total distance traveled (both cars), algebraically:
3S + 3S + 15 = 6S + 15

Total distance traveled (both cars), numerically:
297


Setting that total and the algebraic equation equal to each other, you get the following equation:
6S + 15 = 297

First, subtract 15 from both sides. Then you're left with the following equation:

6S = 282

Divide both sides of that equation by 6, to isolate the variable "S." You're left with the following answer:

S = 47


-----------------------

If S = 47, then S + 5 = 52


So,

the speed of the slower car is 47 mph, and
the speed of the faster car is 52 mph.


Let me know if that makes sense!