Question

An express train makes a run of 240 km at a certain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. Find the speed of the Express train in km/hr

Answer 1

116.9 km/hr

Explanation:

Let the speed of the express train be s and the time required by that train to cover 240 km be t.

Since distance = rate times time,

rate = distance / time

240 km

and so, for the express train, rate = ----------------

t

To solve this problem, find the rate of the express train first.

240 km

For the other train, rate - (12 km/hr) = -----------------

t - 1

Substituting (240 km)/1 for rate in the second equation results in:

240 km 12 km 240 km

------------ - ------------- = ------------------

1 hr 1 hr t - 1

Simplifying the left side, we get:

228 km 240 km

--------------- = -------------

1 hr t - 1

Note that if we multiply 228 km by 1.053, we get 240 km.

Let's multiply both numerator and denominator of the left side of the above equation by 1.053:

240 km 240 km

---------------- = --------------

1.053 hr t - 1

Then t - 1 = 1.053, and t = 2.053 (hours)

We already know that the speed of the first train is

240 km

rate = ----------------

t

and we now know that t = 2.053 hrs.

Thus, the rate of the express train is

240 km

rate = ------------------ = 116.9 km/hr

2.053 hrs t