algebra
posted by Sam .
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?

let her distance covered cycling be x miles
let her distance covered running be 85x miles
time cycling = x/14
time running = (85x)/8
x/14 + (85x)/8 = 6.5
multiply by 56
4x + 7(85x) = 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!