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An express train travelled at an average speed of 100 kmph, stopping for 3 min after 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time it took the express train to travel 600 km ?

An express train travelled at an average speed of 100 kmph, stopping for 3 min after 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 min after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time it took the express train to travel 600 km ? Correct Answer 307.5 km

Time taken by the express train to cover 600 km :
$$ = \left( {\frac{{600}}{{100}}} \right){\text{ hrs}} = 6{\text{ hrs}}$$
Number of stoppages = (600 ÷ 75) - 1 = 7
Duration of stoppage = (3 × 7) min = 21 min
Total time taken = 6 hrs 21 min
Total time taken by local train to cover 50 km (with stoppages)
= 1 hr 2 min
So, the local train covers (50 × 6) = 300 km in 6 hr 12 min
In remaining 9 min, it covers $$ = \left( {\frac{{50}}{{60}} \times 9} \right){\text{ km}} = 7.5{\text{ km}}$$
∴ Required distance = (300 + 7.5) km = 307.5 km

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