Practice FAST-NU Advanced Mathematics questions with answers and explanations.
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The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
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The speed is 90 × 5/18 = 25 m/s, so total distance is 25 × 24 = 600 m.
Subtracting the train length gives a bridge length of 400 m.
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Downwind speed is 300 km/h and upwind speed is 200 km/h.
Wind speed is half their difference: 50 km/h.
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The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
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For equal time intervals, average speed is the arithmetic mean.
Thus, (40 + 60)/2 = 50 km/h.
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For opposite directions, relative speeds are added.
Thus, 50 + 70 = 120 km/h.
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For motion in the same direction, relative speed is the difference.
Thus, 80 - 55 = 25 km/h.
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To pass a pole, the train covers its own length.
Speed = 150 ÷ 10 = 15 m/s.
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The train covers its length plus the platform length: 300 meters.
Speed = 300 ÷ 20 = 15 m/s.
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Total distance is 100 + 140 = 240 meters.
Relative speed is 10 + 14 = 24 m/s, so time = 10 seconds.
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Relative speed is 66 km/h = 55/3 m/s.
Length = speed × time = 55/3 × 18 = 330 meters.
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Downstream speed equals still-water speed plus stream speed.
Thus, 12 + 3 = 15 km/h.
