Question 777658
Beth had planned to run an average of 6 miles per hour in a race. She had a very good race and actually ran at an average speed of 7 miles per hour, finishing 10 minutes sooner than she would have if she had averaged 6 miles per hour. How long was the race?

time taken with speed of 6 mph - time taken with speed of 7 mph =10minutes

t=d/r

let x be the distance of the race
time = x/6 ( planned)

(x/7) = actual time

{{{x/6-x/7=10/60}}}

{{{x/6-x/7 = 1/6}}}

Multiply equation by 42

{{{(x*42)/6 -(x*42)/7 =42/6}}}

{{{7x-6x=7}}}

x=7=> distance