A passenger train 100 meters long clears a line worker tracking on the ballast track in 5 seconds flat when both move along the identical direction. If the line worker walks at 8 km/h, find the train speed. MCQ with Answer and Explanation
A passenger train 100 meters long clears a line worker tracking on the ballast track in 5 seconds flat when both move along the identical direction. If the line worker walks at 8 km/h, find the train speed.
A. 76 km/h
B. 84 km/h
C. 80 km/h
D. 88 km/h
Answer: Option C
Solution (By JKSSB Mock Tests)
Relative tracking speed = 100 / 5 = 20 m/s = 20 * (18/5) = 72 km/h. In identical directions, Relative Speed = Speed of train - Speed of worker => 72 = Speed of train - 8 => Speed of train = 80 km/h.
A boat goes 6 km upstream and returns back to the starting point in 2 hours. If the speed of the stream is 4 km/h, find the speed of the boat in still water.
Explanation:
Let speed of boat in still water be v. 6 / (v - 4) + 6 / (v + 4) = 2 => 3 / (v - 4) + 3 / (v + 4) = 1 => 3(v + 4 + v - 4) = v^2 - 16 => 6v = v^2 - 16 => v^2 - 6v - 16 = 0. Solving the quadratic equation gives (v - 8)(v + 2) = 0. Since speed must be positive, v = 8 km/h.
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