Answer:
116.9 km/hr
Step-by-step 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
