A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time and if the train were slower by 6 km/hr, it

Question

A train covered a certain distance at a uniform speed. If the train would have been 6 km/hr faster, it would have taken 4 hours less than the scheduled time and if the train were slower by 6 km/hr, it would have taken 6 hrs. more than the scheduled time. Find the length of the journey.

Accepted Answer

Step 1: Let usual speed of train be $x$ km/hr and distance covered be $d$ km. Therefore $\frac{d}{x + 6} = \frac{d}{x} - 4$ ... (i)
Step 2: $\frac{d}{x - 6} = \frac{d}{x} + 6$ ... (ii)
Step 3: Solving (i) and (ii): $x = 30$ and $d = 720$

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