A train travels at a certain average speed for a distance of 63 km ...

Question : A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed?

Doubt by Jaskirat

Solution :

Case I

Let the original speed of the train be x km/h

Distance covered = 63 km
Speed = Distance / Time
Time = Distance/Speed
t₁=63/x — (1)

Case II
New Speed = (x+6) km/h
Distance Covered = 72 km

t₂=72/(x+6) — (2)

ATQ
t₁+t₂=3

x²+6x=45x+126

x²+6x-45x-126=0

x²-39x-126=0

x²-(42-3)x-126=0

x²-42x+3x-126=0

x(x-42)+3(x-42)=0

(x-3)(x-42)=0

x-3=0

x=-3

But speed can't be negative.

so x=-3 is rejected.

x-42=0

x=42 km/h

Hence, original speed of the train is 42 km/h.

Class 10

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A train travels at a certain average speed for a distance of 63 km ...