SOLUTION: On a 135-mile bicycle trip, John averaged 5 miles per hour faster for the first 60 miles than he did for the last 75 miles. The entire trip took eight hours. Find his rate for the

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Question 296668: On a 135-mile bicycle trip, John averaged 5 miles per hour faster for the first 60 miles than he did for the last 75 miles. The entire trip took eight hours. Find his rate for the first 60 miles.
Found 2 solutions by richwmiller, checkley77:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x+5)*y=60
x*z=75
y+z=8
x = 15, y = 3, z = 5
20 mph first 60 miles
check
20*3=60
5*15=75
3+5=8
ok

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
T=D/R
8=60/(R+5)+75/R
8=[(60R+75(R+5)]/R(R+5)
8=[60R+75R+375]/R^2+5R
8(R^2+5R)=135R+375
8R^2+40R-135R-375=0
8R^2-95R-375=0
(x-15)(8x+25)=0
x-15=0
x=15 mph is the speed for the 75 mile leg.
15+5=20mph is the speed for the 60 mile leg.