Question

A train travels the first 30 kilometre of 120 kilometre with a uniform speed of 30 kilometre per hour what should be the speed to cover the remaining distance of the track so that its average speed is 60 kilometre per hour for entire trip

Answer 1

Total Distance=120 km

Average Speed=60 km/h

30 km at=30 km/h

Time=Distance÷speed

Time Taken to Cover 30 km

30÷30

=1

Time Taken=1 hour.

Now Remaining Distance=120-30=90 km

Let Speed=x km/h

Time=90/X hours

We know

$\boxed{\mathtt{Average\:Speed=Total\: Distance\:\div\:Total\: Time}}$

Total Time=1 hour +90/X hour

Average Speed

$120 \div (1 + \frac{90}{x} ) = 60 \\ \\ 120 \div ( \frac{x + 90}{x} ) = 60 \\ \\ 120 \times \frac{x}{x + 90} = 60 \\ \\ \frac{120x}{x + 90} = 60 \\ \\ 120x = 60(x + 90) \\ \\ 120x = 60x + 5400 \\ \\ 120x - 60x = 5400 \\ \\ 60x = 5400 \\ \\ x = \frac{5400}{60} \\ \\ = 90$

*Note LCM=X

X=90

Speed for 90 km=X=90 km/h

$\boxed{\mathbf{\huge{Speed=90\:km/h}}}$