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. MCQ with Answer and Explanation
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.
A. 6 km/h
B. 10 km/h
C. 8 km/h
D. 12 km/h
Answer: Option C
Solution (By JKSSB Mock Tests)
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.
A train leaves a station at 4:00 PM and travels at an average speed of 60 km/h. Another train leaves the same station at 5:00 PM in the same direction at an average speed of 80 km/h. At what time will the second train catch up with the first train?
Explanation:
By 5:00 PM, the first train has traveled for 1 hour and covered 60 km. Relative speed = 80 - 60 = 20 km/h. Time needed to catch up = 60 / 20 = 3 hours. Catch up time = 5:00 PM + 3 hours = 8:00 PM.
Explanation:
New speed = 6/7 of typical speed => New time = 7/6 of typical time. Difference = 1/6 of typical time = 14 minutes. Typical time = 14 * 6 = 84 minutes.
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