Find both speeds?

Question

A train travels 150 kilometers in the same time that a plan covers 400 kilo meters. If the speed of the plan is 20 km per hour less than 3 times the speed of train. Find both speeds?

Answer 1

First set up your variables:

 

Let t = the speed of the train, and

let p = the speed of the plane.

 

Since time = distance / speed, the time is takes for the train to travel 150 km is 150 / t, and the time it takes for the plane to cover 400 km is 400 / p.  They told you that they cover these distances in the same amount of time, so that means that 150 / t = 400 / p.

 

They also tell you the p = 3t - 20.  Do you see how?  ("...the speed of the plan is 20 km per hour less than 3 times the speed of train.")

 

So that gives you 2 equations you can solve together:

 

150 / t = 400 / p

p = 3t - 20

 

Get the variables in the numerators in the first equation, by multiplying both sides by tp

150p = 400t

 

The second equation gives you a value for p, so substitute it into the new first equation:

150 (3t - 20) = 400t

 

Simplify:

450t - 3000 = 400t

 

Continue to solve:

50t - 3000 = 0

50t = 3000

t = 60

 

p = 3t - 20 = 3*60  - 20 = 180 - 20 = 160.

 

So the speed of the train is 60 km/h and the speed of the plane is 160 km/h.