SOLUTION: Zeke's motor cycle traveled 270 miles at a certain speed. Had he gone 15 mph faster, the trip would have taken 3 hours less. Find the speed of the motorcycle.

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Question 250722: Zeke's motor cycle traveled 270 miles at a certain speed. Had he gone 15 mph faster, the trip would have taken 3 hours less. Find the speed of the motorcycle.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
This is an RTD problem. Here is the table
vehicle . . . . . . . rate . . . . . . . . time . . . . . . . .distance
cycle . . . . . . . . . R . . . . . . .. . . 270/R . . . . . .. 270
cycle . . . . . . . . .R + 15 . .. . . . 270/R - 3 . . . .. 270
I let R = rate. The first time is D / R = 270 / R. All times are in hours, so the second time is
(270/R - 3) hours.
Look at the second line.
(R + 15)(270/R - 3) = 270
By FOIL, we get
270 - 3R + 4050/R - 45 = 270
multiply both sides by R. we get
270R - 3R^2 + 4050 - 45R = 270R.
Simplify to get
3R^2 + 45R - 4050 = 0
dividing by 3, we get
R^2 + 15R - 1350 = 0
factoring, we get
(R + 45)(R - 30) = 0
R = -45 or R = 30.
we can use -45, so
R = 30. The motorcycle was traveling at 30 mph.