A train travels 150 kilometers in the same time that a plane

A train travels 150 kilometers in the same time that a plane covers 400 kilometers. If the speed of the plane is 20 kilometers per hour less than 3 times the speed of the train, find both speeds.

Solution

Velocity = Distance / Time
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v(p) = d/t = 400/t
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v(t) = d/t = 150/t,,,,,note both times are same
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v(p)/ v(t) = 400/150 =2.67,,,,or v(p) = 2.67 v(t)
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v(p) = 3v(t) -20,,,,,,given
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subst from above
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(2.67 v(t) = 3v(t) -20
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-1/3 v(t) = -20
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v(t) = + 60 km /hr,,,,,,,,,v(p) = 3*60-20 = 160 km/hr
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Check, 60=150/t,,,,t= 2.5 hrs,,,train
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160=400/t,,,,,,t= 2.5 hrs ,,,,,plane ok
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160 = 3(60) -20 ,,,,,,ok