Question 31

A boy covers a certain distance on a toy train. If the train moved 4 kmph faster, it would take 30 minutes less. If it moved 2 kmph slower, it would have taken 20 minutes more. The distance is

Solution

Let the speed be "v" kmph , and time taken be 't' hours to cover distance of D kms.

D = v(t)

1. If the train moved 4 kmph faster, it would take 30 minutes less : D = (v + 4)(t - 0.5)
2. If it moved 2 kmph slower, it would have taken 20 minutes more : D = (v - 2)(t + 0.33)

Now, D = vt + 4t -v/2 - 2
By substituting D = Vt in the above equation : V = 8t - 4

Similarly, D = Vt -2t + 0.33(V) - 0.66
By substituting D = Vt in the just above equation : 2t = 0.33(v) - 0.66
: V = 2 + 6t

Therefore, (8t - 4) = (2 + 6t)
Hence, t = 3 hours
So, V = 2 + 6(3) = 20 kmph

Therefore, Distance (D) = V(t) = 20(3) = 60 kms.

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