Question

Gabrielle went on a 72 mile trip to a soccer game. On the way back, due to road construction she had to drive 18 miles per hour slower. This made the trip take 9 hours longer. How fast did she drive to the soccer game?

Answer 1

Gabrielle drove to the soccer game at the speed of 18 miles/hour

Explanation:

Given: Distance covered = 72 miles

On the way back, she had to drive 18 miles per hour slower due to road construction which made the trip take 9 hours longer.

To find: speed

Solution:

Let speed be x miles/hour

Time taken = distance covered/time taken =
`(72)/(x)` hours

On the way back, she had to drive 18 miles per hour slower due to road construction

So, new speed = ( x - 18 ) miles/hour

Time taken as per new speed =
`(72)/(x-18)` hours

According to question,

`(72)/(x-18)-(72)/(x)=9\\(1)/(x-18)-(1)/(x)=(9)/(72)\\(x-x+18)/(x(x-18))=(1)/(8)\\x^2-18x-144=0\\x^2-24x+6x-144=0\\x(x-18)+6(x-18)=0\\(x-18)(x+6)=0\\x=18\,,\,-6`

Being a speed, x can not be negative. So,
`x=-6` is rejected

So,

Gabrielle drove to the soccer game at the speed of 18 miles/hour