(Rational expression word probelm) One car travels 20km/hr faster....

Question

One car travels 20 km/hr faster than another.  While one car travels 225 km, the other one travels 325 km.  Find their speeds.

Answer 1

Let's let v be the speed of the slower car.  Then, v + 25 is the speed of the faster one.

Dimensionally, speed is distance divided by time.  Distance divided by speed is distance divided by (distance divided by time), so distance divided by speed is time.  The two vehicles traveled different distances in the same time, so our equation then looks like this:

225/v = 325/(v+25)

Cross-multiplying to clear the denominators, we get:

225v + 5625 = 325v

Subtracting 225v from both sides, we get:

 

5625 = 100v

Dividing by 100, we get

56.25 = v

Plugging that back in, we see that the slower car does 225 km in 4 hours, and the faster car, driving at 81.25 km/hr, goes 325 km in 4 hours - it works.