Question

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

Answer 1

Two identical trains, Train A and Train B, are traveling along parallel rails.

The speed of Train A is 88 km/hr, and the speed of Train B is 96 km/hr. Based on this information, which of the following statements is true?

A.

Train B has more kinetic energy than Train A.

B.

Train A has more kinetic energy than Train B.

C.

The trains have the same kinetic energy.

D.

Neither train has any kinetic energy.

Explanation:

Answer 2

• train: 40 kph
• plane: 140 kph

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.