Explanation:
Distance for A to run = 500 - 140 = 360 meters. Ratio of speeds A:B = 3:4. Time taken by A to run 360m is proportional to 360 / 3 = 120 units. In the same time, B runs 4 * 120 = 480 meters. B needs 500m to win but only reaches 480m. Thus, A wins, and B is 500 - 480 = 20 meters behind. A wins by 20 meters.
A local train spans a track sector in 40 minutes. If its speed is lowered by 6 km/h, it tracks the same sector in 45 minutes. Find the distance of this track sector.
A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours 30 minutes. Find the speed of the boat in still water.
Explanation:
Let 1/u = x and 1/d = y. 24x + 28y = 6 and 30x + 21y = 6.5. Solving these linear equations gives x = 1/6 and y = 1/14. So upstream speed u = 6 km/h, downstream speed d = 14 km/h. Speed in still water = (d + u)/2 = (14 + 6)/2 = 10 km/h.
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