CMA Foundation · Fundamentals of Business Mathematics and Statistics · Time and Distance
A boat covers 24 km upstream and 36 km downstream in 6 hours. It also covers 36 km upstream and 24 km downstream in 6.5 hours. What is the speed of the boat in still water?
The boat's still-water speed is 10 km/h. Solving the two time equations gives an upstream speed of 8 km/h and a downstream speed of 12 km/h. Still-water speed is their average, (12 + 8)/2 = 10 km/h, and both given journeys check out.
- A10 km/hCorrect
- B12 km/h
- C9 km/h
- D8 km/h
Explanation
Let upstream speed u and downstream speed v. 24/u + 36/v = 6 and 36/u + 24/v = 6.5. Let x = 1/u, y = 1/v: 24x+36y=6, 36x+24y=6.5. Adding: 60(x+y)=12.5, x+y=5/24. Subtracting: 12(x-y)=0.5, x-y=1/24. So x=1/8, y=1/12, giving u=8, v=12. Still-water speed = (12+8)/2 = 10 km/h. Check: 24/8+36/12=3+3=6; 36/8+24/12=4.5+2=6.5.
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