Discussion
Jammu Express is 1.2 km long and is running along the Kerala express at speed of 80km/hr. Kerala express is 2/3rd the length of Jammu express and runs at 60 km/hr. How much time will it take for Jammu express to overtake the Kerala express?
Answer: B
Trains moving in the same direction close at the difference of their speeds; in opposite directions, at the sum.
\[ \text{Kerala express length} = \frac{2}{3} \times 1200 = 800 \text{ m} \]
\[ \text{relative speed} = 80 - 60 = 20 \text{ km/hr} = 20 \times \frac{5}{18} = \frac{50}{9} \text{ m/s} \]
To overtake, the Jammu express must cover both lengths:
\[ t = \frac{1200 + 800}{50/9} = \frac{2000 \times 9}{50} = 360 \text{ s} = 6 \text{ minutes} \]
Overtaking always needs the sum of the lengths, even though the speeds subtract.
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