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distance = speed * time
Let t = the correct amount of time for the train to run
t+11 = When the train is 11 minutes behind
t+5 = When the train is 5 minutes behind
Speed when 11 minutes behind = 40
Speed when 5 minutes behind = 50

In both instances, the train covers the same distance

(t+11)(40) = (t+5)(50)
t= 19
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Bunuel
If a train runs at 40 km/h, it reaches its destination late by 11 min but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey is

(A) 13 min
(B) 15 min
(C) 19 min
(D) 21 min
(E) 22 min
Solution:

The train will travel the same distance for the two trips, so we can use the equation rate_1 x time_1 = rate_2 x time_2. Let’s let t be the correct time for the train to complete the journey, in hours. We see that for the slower trip, the time will be (t +11/60) hours, and for the faster trip, the time will be (t + 5/60) hours. :

rate_1 x time_1 = rate_2 x time_2

40(t + 11/60) = 50(t + 5/60)

40t + 44/6 = 50t + 25/6

19/6 = 10t

19/60 = t

Therefore, the correct time is 19/60 of an hour, or 19 minutes.

Answer: C
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