SOLUTION: a train travels 200km in the same time that a plane covers 900km. If the speed of the plane is 20km per hour less than 5 times the speed of the train find both speed

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Question 1119129: a train travels 200km in the same time that a plane covers 900km. If the speed of the plane is 20km per hour less than 5 times the speed of the train find both speed
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed of train
-20+5r, speed of plane


200%2Fr=900%2F%285r-20%29
-
200%2Fr=180%2F%28r-4%29

10%2Fr=9%2F%28r-4%29

10%28r-4%29=9r
10r-40=9r
highlight%28r=40%29-------train speed, kilometers per hour

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the speed of the train in km/hr.

Then the distances traveled in equal amounts of time tell us the speed of the plane is (9/2)x.

And the statement of the problem tells us the speed of the plane is 5x-20.

We have two expressions for the speed of the plane; they must be equal. So

%289%2F2%29x+=+5x-20
%28-1%2F2%29x+=+-20
x+=+40

The speed of the train is 40km/hr; the speed of the plane is (9/2)*40 = 180km/hr.