Question

A train covers a distance in 50 min, if it runs at a speed of 48 kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 min.

Answer 1

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We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.

Time = 50/60 hr = $\dfrac{5}{6}$hr

Speed = 48 mph

Distance = S×T = 48 ×$\dfrac{5}{6}$= 40 km

New time will be 40 minutes so,

Time = $\dfrac{40}{60} hr = \dfrac{2}{3} hr$

Now we know, 
Speed = Distance/Time

New speed = 40×$\dfrac{3}{2}$kmph = 60kmph

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Answer 2

Given : The Speed of Train is 48 kmph

⇒ In One Hour, The Train Travels a Distance of 48 km

⇒ In 60 Minutes, The Train Travels a Distance of 48 km

⇒ In 50 Minutes, The Train Travels a Distance of : $[\frac{50 \times 48}{60}] = 40\;km$

Now, We need to find out the speed at which the train must run in order reduce the time of journey of 40 km to 40 Minutes

We know that : 40 Minutes is : $\frac{2}{3}\;hr$

We know that : $Speed = \frac{Distance\;travelled}{Time\;taken}$

⇒ $Speed = \frac{40}{\frac{2}{3}} = \frac{120}{2} = 60\;kmph$

So, The Speed at which the train must run is 60 kmph