Math word problem

Question

a train travels 180km in the same time that a plan covers 810km if the speed of the plane is 20km per hr less than 5 times the speed of the train find both speeds?

Answer 1

We know that distance = rate x time

 

So, time = distance/rate

 

For the train, let its rate = x. Its distance traveled is 180 km, so:

 

time traveled by train = 180/x

 

The rate of the plane is 5x - 20, and it traveled 810 km in the same amount of time, so we have:

 

time traveled by plane = 810/(5x - 20)

 

Since the plane and train traveled for the same amount of time, we can set these two equal to each other.

 

180/x = 810/(5x - 20)

810x = 180(5x - 20)

810x = 900x - 3600

-90x = -3600

x = 40 km/h = speed of train

 

The plane's speed is 5x - 20 = 5(40) - 20 = 200 - 20 = 180 km/h