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The speed of a passenger train is 20 mph faster than the speed of a freight train. The passenger train travels 290 miles in the same time it takes the freight train to
travel 190 miles. Find the speed of each train.
The speed of the passenger train is 60 mph.
The speed of the freight train is 40 mph.

Answer 1

Explanation:

Let +s+ = the speed of the passenger train

+s+-+20%5D+ = the speed of the freight train

Let +t+ = time in hours for both trains

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Equation forpassenger train:

(1) +280+=+s%2At+

Equation for freight train:

(2) +180+=+%28+s-20+%29%2At+

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(1) +t+=+280%2Fs+

Substitute (1) into (2)

(2) +180+=+%28+s-20+%29%2A%28+280%2Fs+%29+

(2) +180s+=+280s+-+5600+

(2) +100s+=+5600+

(2) +s+=+56+

and

+s+-+20+=+36+

The speed of the passenger train is 56 mi/hr

The speed of the freight train is 36 mi/hr

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check:

(1) +280+=+56%2At+

(1) +t+=+5+

and

(2) +180+=+%28+56-20+%29%2At+

(2) +180+=+36t+

(2) +t+=+5+

OK