Question

A train travels the first 30 km of 120 km track with uniform speed of 30 km / h . What should be the speed of the train to cover the remaining distance of the track so that its average speed is 60 km/h for the entire trip?​

Answer 1

Total Distance=120 km

Train Had Travelled =30 km

30 km at=30 km/h

Time=Distance/Speed

Time=30/30

Time=1 hour

Means Train Travels 30 km in 1 hour

Remaining Distance to Cover 120-30=90 km

Let Train Travels 90 km at x km/h

Time taken=90/x hours

Average Speed Should be=60 km/h

$Average \: Speed = \frac{total \: distance}{total \: time \: taken}$

Total Distance=120 km

Total Time=(1+90/x) hours

Average Speed=60 km/h

$60 = \frac{120}{1 + \frac{90}{x} } \\ \\ 60(1 + \frac{90}{x} ) = 120 \\ \\ 1 + \frac{90}{x} = \frac{120}{60} \\ \\ 1 + \frac{90}{x} = 2 \\ \\ \frac{90}{x} = 2 - 1 \\ \\ \frac{90}{x} = 1 \\ \\ x = 90$

Speed Should be x km/h=90 km/h

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