A train travels 110 km in the same time that a plane covers 385 km. If the speed of the plane is 20 km per hr less than 4 times the speed of the train, find the speeds.
Trains speed: __ km per hr
Plane's speed — km per hr

Step-by-step explanation:

Let t represent the speed of the train in km/h. Then 4t-20 is the speed of the plane. Travel times are the same, so we can use the formula ...

  time = distance/speed

and equate the travel times.

  110/t = 385/(4t-20)

Cross multiplying gives ...

  110(4t -20) = 385t

  440t -2200 = 385t . . . . . eliminate parentheses

  55t -2200 = 0 . . . . . . . . . subtract 385t

  t -40 = 0 . . . . . . . . . divide by 55

  t = 40 . . . . . . . . . . . add 40; train's speed is 40 kph

  4t -20 = 140 . . . . . . find plane's speed; 140 kph

The train's speed is 40 km/h; the plane's speed is 140 km/h.

Check

Train's travel time = 110 km/(40 km/h) = 2.75 h.

Plane's travel time = 385 km/(140 km/h) = 2.75 h.

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