Lesson One more problem on calculating an average speed

One more problem on calculating an average speed

Problem 1

Let D be the entire distance.

The train covered first 80% of the entire distance, i.e. 0.8*D, at the average speed of 120 . 
Hence, it spent  hours to cover this part. 

Let u be the speed of the train on the second (20%) part of the trip.
Then the train spent  hours to cover the second part. 

Thus the full time for the trip was

t =  +     (1)

hours. We are given that the average speed was 90 . 
It means that the whole distance divided by the full time is 90 . 

It gives you an equation

 = 90.

Cancel the factor D in the numerator and the denominator. You will get

 = 90.

It is your equation to find the speed u.

Let us simplify it step by step:

 = 90  ----->   = 3  ----->  4u = 3*(0.8*u + 24)  ----->  4u = 2.4u + 72  ----->  4u - 2.4 u = 72  ----->  1.6u = 72,

u =  = 45 . 

Thus the speed of the train on the second part of the trip is 45 .

The solution is completed.

Answer. The speed of the train on the second part of the trip was 45 .