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2 trains each of length 120 metres move in the same direction. The faster train completely overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, faster train would overtake it in 10 seconds. Find the speeds of the two trains (faster and slower respectively in m/s)
A. 48 and 16
B. 32 and 16
C. 48 and 32
D. 64 and 48
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2 trains each of length 120 metres move in the same direction. The faster train completely overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, faster train would overtake it in 10 seconds. Find the speeds of the two trains (faster and slower respectively in m/s)
A. 48 and 16
B. 32 and 16
C. 48 and 32
D. 64 and 48
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Formula to find time to cross each other: When 2 trains of lengths \(a\) \(meters\) and \(b\) \(meters\) are moving in same direction with speeds \(x\) \(m/s\) and \(y\) \(m/s\) respectively \((x > y)\), then the time taken to cross each other is \(= \frac{a + b}{x - y}\)
Given; 2 trains each of length \(120\) \(meters\). Let the speed of faster train be \(x\) \(m/s\) and slower train be \(y\) \(m/s\).
Given, faster train completely overtakes the slower one in \(15\) \(seconds\). ie; time taken to cross each other = \(15 s\) \(15 = \frac{120 + 120}{x - y}\) \(==>\) \(\frac{240}{x - y}\) \(x - y = 16\) \(y = x - 16\) -------------- (i)
If the slower train were to move at half its speed, faster train would overtake it in \(10\) \(seconds\). Speed of slower train would become \(y/2\). \(10 = \frac{240}{x - {y/2}}==>\) \(x - \frac{y}{2} = 24\) \(==>\) \(\frac{2x - y}{2}= 24\) \(==>\) \(2x - y = 48\) -------------------- (ii)
Substituting value of \(y\) from (i) in above equation (ii); \(2x - (x - 16) = 48\) ==> \(2x - x + 16 = 48\) \(x = 48 - 16 = 32\)
Therefore speed of faster train is \(32 m/s\) Speed of slower train, \(y = x - 16\) \(==> 32 - 16 = 16\). Speeds of trains are \(32\) \(m/s\) and \(16\) \(m/s\). Answer B...
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