Answer:
Gabrielle drove to the soccer game at the speed of 18 miles/hour
Step-by-step 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 = [tex]\frac{72}{x}[/tex] 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 = [tex]\frac{72}{x-18}[/tex] hours
According to question,
[tex]\frac{72}{x-18}-\frac{72}{x}=9\\\frac{1}{x-18}-\frac{1}{x}=\frac{9}{72}\\\frac{x-x+18}{x(x-18)}=\frac{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[/tex]
Being a speed, x can not be negative. So, [tex]x=-6[/tex] is rejected
So,
Gabrielle drove to the soccer game at the speed of 18 miles/hour
