Question

A student travels 420 km in 7 hrs he travels for some time @75 km /hr and the rest of time @55 km /hr how long did he travel at the higher speed

Answer 1

Answer:

Assumption:

Let Td, Tt, Hs, Ls denote the variables as below.

Let average speed be denoted by Sa

Let X be the distance traveled in 75 km/hr and Y be the distance traveled in 55km/hr.

Given:  

Total distance travelled (Td) = 420 km

Total time taken (Tt) = 7 hours

Higher Speed (Hs) = 75 km/hr

Lower Speed (Ls) = 55 km/hr

Therefore,

Average Speed (Sa) = 420/7 = 60 km/hr

The ratio of the difference between Hs and Ls to the average speed Sa is 1:3 (60-55 = 5 and 75-60=15. Hence 1:3)

Hence, The distance traveled in the lower speed is 3 times more than the distance traveled in high speed.  

Let X be the distance traveled in 75 km/hr and Y be the distance traveled in 55 km/hr.

As proved above, Y=3X

So, X+Y = 420

X+3X=420

X=105 kms

Y = 3(105) = 315 kms

Hence,

The distance traveled in 75 km/hr = 105 km and the distance traveled in 55 km/hr is 315 km.