Math word Problem

Question

Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 8 miles per hour faster than on her way home. If Jen spent a total of 2 hours bicycling, find the two rates (rate of speed for the way there and rate of speed for the way home)

Answer 1

Let : x=time to and y=time from....x+y=2

Let T=speed to and H=time from T=H+8

xT = yH = 6

y=6/H and x = 6/T = 6/(H+8)

(6/H) + [6/(H+8)] = 2

6H + 48 + 6H = 2H² + 16H

2H² + 4H - 48 = 0 => H² + 2H - 24 =0

H = [-2 + sqrt(4+96)]/2 = 4

T = 12

y=6/4 = 3/2

x=6/12 = 1/2

x+y = 4 as required