A passenger train leaves the station 1 hour after a freight train leaves the same station. The freight train is traveling 16 mph slower than the passenger train. Find the rate of both trains if it takes 2 hours for the passenger train to overtake the freight train.

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jitushashi143 jitushashi143 · Answer 1 · 2019-12-20T07:13:42+01:00

Answer:

Rate of the passenger train is [tex]48\ mph[/tex] and the rate of the freight train is [tex]32\ mph[/tex]

Step-by-step explanation:

Let the speed of the passenger train be [tex]x\ mph[/tex]

Speed of the freight train be [tex](x-16)\ mph[/tex]

Note:

If the passenger train overtakes the freight train than at the point both have traveled same distance as they are from the same station.

And [tex]Distance=Speed\times time[/tex]

Time taken by the passenger train to reach that point [tex]=2\ hrs[/tex]

Time taken by freight train,= (time taken by the passenger train + time elapsed) [tex]=(2+1)=3\ hrs[/tex]

Re-arranging the terms.

Distances are same.

[tex]3(x-16)=2(x)[/tex]

[tex]3x-48=2x[/tex]

Subtracting [tex]2x[/tex] both sides.

[tex]3x-2x=48[/tex]

[tex]x=48\ mph[/tex]

So the rate of the passenger train is [tex]x\ mph=48\ mph[/tex] and the rate of the freight train is [tex](x-160)\ mph =(48-16)=32\ mph[/tex]