Each of two cars, whose average rates are in the ratio of 4:5, travels the distance of 160 miles. If the fast car travels 1/2 an hour less than the slow car, find the average rate of each car.

64 mph and 80 mph

Step-by-step explanation:

rate1 : rate 2

4x : 5x

The time for car 1 = t

time for car 2 = t-1/2

Both cars travel 160 miles

We know the formula d=rt

Car 1

160 = 4x*t

Car 2

160 = 5x * (t-1/2)

Since both equations equal 160 miles, we can set them equal

4xt = 5x (t-1/2)

Divide each side by x

4xt/x = 5x (t-1/2) / x

4t = 5 (t-1/2)

Distribute

4t = 5t - 5/2

Subtract 5t from each side

4t-5t = 5t-5t - 5/2

-t = - 5/2

Multiply by - 1

t = 5/2

We know the time, now using our equation for distance

160 = 4x*t

160 = 4x*5/2

160 = 10x

Divide each side by 10

160/10 = 10x/0

16 = x

Now we can find each cars rate

rate1 : rate 2

4x : 5x

4*16: 5*16

64:80