Autumn went on a 24 mile trip to a soccer game. On the way back, due to road construction she had to drive 3 miles per hour slower. This made the trip take 4 ho

Question

Autumn went on a 24 mile trip to a soccer game. On the way back, due to road construction she had to drive 3 miles per hour slower. This made the trip take 4 hours longer. How fast did she drive to the soccer game?

Answer 1

This is essentially the same problem as Andrew, but with different numbers.

 

time = 24/s

 

If speed is decreased by 3 (s - 3), then the time is increased by 4  (24/s + 4). The distance is still 24 miles, so

 

(s-3)(24/s + 4) = 24

 

Multiply both sides by s to get     (s-3)(24/s + 4)s = 24s

 

(s-3)(24+4s) = 24s

 

24s - 72 + 4s² - 12s = 24s

 

Subtract 24s from both sides and rearrange the terms:

 

4s² - 12s - 72 = 0

 

Divide both sides by 4:     s² - 3s - 18 = 0

 

Factor:     (s-6)(s+3) = 0

 

So s = 6 mph or s = -3 mph. The speed can't be negative, so her speed was 6 mph and it took her 4 hours. This is not much of a speed. I suspect she rode a bike, like Andrew did.

 

We should check the answer in the words of the problem. If she went 3 mph slower, her speed would be 3 mph (She could walk faster than that!), and it would take 8 hours to go the 24 miles. This is definitely 4 hours more than the 4 hours it took, so the answer checks.