As part of her training routine for basketball, Shaylle alternates between cycling and running for exercise. She cycles at a rate of 14 mph and runs at a rate of 8 mph. If she spends 6.5 hours exercising and covers a total of 85 miles, how much time did she spend on each exercise?

Answer 1

let her distance covered cycling be x miles
let her distance covered running be 85-x miles
time cycling = x/14
time running = (85-x)/8

x/14 + (85-x)/8 = 6.5
multiply by 56

4x + 7(85-x) = 364
4x + 595 - 7x = 364
-3x = -231
x = 77

so she cycled 77 miles
and ran 8 miles

time cycling = 77/14 = 5.5 hrs
time running = 8/8 = 1 hour

total time = 6.5 hrs , checks out!