SOLUTION: Over a distance of 120 km , the average speed of a train 40 kmh faster than the speed of a car. If The train covers the distance in 30 minutes less time , find the speed of The tr

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Question 1153877: Over a distance of 120 km , the average speed of a train 40 kmh faster than the speed of a car. If The train covers the distance in 30 minutes less time , find the speed of The train?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                   SPEED         TIME           DISTANCE

TRAIN              r+40          120/(r+40)       120

CAR                r             120/r            120

DIFFERENCE                      1%2F2

Thirty minutes is one-half hour.

The train's time is less than car's time by half hour.
120%2Fr-120%2F%28r%2B40%29=1%2F2.
Solve for r+40.
(But can be arranged differently.)
-
240%2Fr-240%2F%28r%2B40%29=1
240%28r%2B40%29-240r=r%5E2%2B40r
240r%2B240%2A40-240r=r%5E2%2B40r
240%2A40=r%5E2%2B40r
r%5E2%2B40r-40%2A240=0
r%5E2%2B40r-9600=0
%28r-80%29%28r%2B120%29=0.
.