Bunuel wrote:
Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in opposite direction. Find the speed of the faster train.
A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph
Let the two speeds be v1 and v2, with v1 > v2.
Same direction: If we treat v2 as stationary, the speed of the faster train is effectively v1 - v2. The faster train needs to travel 200 meters to fully cross the slower train (since each train is 100 meters long). Then \(\frac{200 }{ {v1 - v2}} = 60\) seconds.
Opposite direction: If we treat either stationary, the speed of the other train is effectively v1 + v2. Then \(\frac{200 }{ {v1 + v2}} = 10\) seconds.
So we get \(v1 + v2 = 20\) m/s and \(v1 - v2 = 10/3\) m/s. We can add the equations to get \(2* v1 = 70/3\) m/s and \(v1 = 35/3\) m/s . Finally convert to kmph by multiplying \(\frac{{1 km} }{ {1000 m}}\) and \(\frac{{3600 s} }{ {1 h}}\),
\(\frac{35}{3} * \frac{3600 }{ 1000} = 35 * \frac{1200 }{ 1000} = 35 * \frac{6 }{ 5} = 42\)
Ans: C
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