SOLUTION: A plane can fly 300 miles in the same time as it takes a car to go 180 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A plane can fly 300 miles in the same time as it takes a car to go 180 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.       Log On


   

Question 1114941: A plane can fly 300 miles in the same time as it takes a car to go 180 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for both the
plane and the car
Let +s+ = the speed of the plane in mi/hr
+s+-+90+ = the speed in mi/hr of the car
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Equation for the plane:
(1) +300+=+s%2At+
Equation for the car:
(2) +180+=+%28+s-90+%29%2At+
--------------------------
(1) +s+=+300%2Ft+
Plug (1) into (2)
(2) +180+=+%28+300%2Ft+-+90+%29%2At+
(2) +180+=+300+-+90t+
(2) +90t+=+120+
(2) +t+=+4%2F3+
and
(1) +s+=+300%2Ft+
(1) +s+=+300%2F%284%2F3%29+
(1) +s+=+900%2F4+
(1) +s+=+225+
The speed of the plane is 225 mi/hr
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check:
(1) +300+=+s%2At+
(1) +300+=+225%2A%28+4%2F3+%29+
(1) +3%2A300+=+4%2A225+
(1) +900+=+900+
and
(2) ++180+=+%28+s-90+%29%2At+
(2) +180+=+%28+225+-+90+%29%2A%284%2F3%29+
(2) +180+=+135%2A%284%2F3%29+
(2) +540+=+540+
OK