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AditiDeokar
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Schools: NUS ESSEC MiM '26 ESSEC MiF '26 INSEAD MiM '26 ESADE Imperial ISB '26 ESADE HEC Sept '26 IE INSEAD Jan '26
GMAT Focus 1: 525 Q77 V77 DI74
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20 Dec 2025, 23:53
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This problem took me a long time to fully understand, especially the second meeting point, below is the solution.
Train A and B are at opposite ends 120 miles apart, Train A travels at speed of 30 miles per hour while Train B travels at 90 miles per hour, individually each train will take 4hrs and 1.3hrs respectively to reach either end, therefore Train B (the faster one) can encouter train A twice (round trip - 240 miles/90 = 8/3 hrs which is less than 4 hours). The first encounter would be when Distance by relative speed (opposite directions means we add the speeds - 120 miles/120mph = 1hr, they encounter each other 1hr into journey. Take the easier calc one Train A - 30mph, travels 30 miles in 1hr, so they meet 30 miles away from DC. Now Train B has to cover the 30 miles to turn around and catch up with Train A for the second encounter, during this time - 30 = 90 x T = 1/3 hrs, Train A has travelled 10 more miles from the 30 miles where it was before, now train B is at Washington DC, Train A is 40 miles from DC, to catch up to train A it will take B : 40 miles /60mph - 2/3 hours, in 2/3 hours Train A would've travelled 20 more miles making the second encounter 60 miles from DC. 60-30 = 30 miles.
Train A and B are at opposite ends 120 miles apart, Train A travels at speed of 30 miles per hour while Train B travels at 90 miles per hour, individually each train will take 4hrs and 1.3hrs respectively to reach either end, therefore Train B (the faster one) can encouter train A twice (round trip - 240 miles/90 = 8/3 hrs which is less than 4 hours). The first encounter would be when Distance by relative speed (opposite directions means we add the speeds - 120 miles/120mph = 1hr, they encounter each other 1hr into journey. Take the easier calc one Train A - 30mph, travels 30 miles in 1hr, so they meet 30 miles away from DC. Now Train B has to cover the 30 miles to turn around and catch up with Train A for the second encounter, during this time - 30 = 90 x T = 1/3 hrs, Train A has travelled 10 more miles from the 30 miles where it was before, now train B is at Washington DC, Train A is 40 miles from DC, to catch up to train A it will take B : 40 miles /60mph - 2/3 hours, in 2/3 hours Train A would've travelled 20 more miles making the second encounter 60 miles from DC. 60-30 = 30 miles.
