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A boat covers a certain distance downstream in 5 hours but takes 7 hours to return upstream to the starting point. If the speed of the stream is 3 km/h, then find the speed of the boat.
20 km/h
24 km/h
18 km/h
26 km/h
48 km/h
- The boat's speed is combined with the stream's speed when traveling downstream.
- Conversely, the stream's speed is subtracted from the boat's speed when moving upstream.
- Let the boat's speed in still water be \( x \) km/h.
- Downstream speed = \( x + 3 \) km/h and time taken = 5 hours.
- Upstream speed = \( x - 3 \) km/h and time taken = 7 hours.
- Distance calculation for both:
$$ \text{Distance} = \text{Speed} \times \text{Time} $$
- For downstream: \( (x + 3) \times 5 = \text{Distance} \)
- For upstream: \( (x - 3) \times 7 = \text{Distance} \)
- Setting equations equal:
$$ 5(x + 3) = 7(x - 3) $$
- Solving for \( x \):
$$ 5x + 15 = 7x - 21 $$
$$ 36 = 2x $$
$$ x = 18 $$
- Thus, the speed of the boat is 18 km/h
By: Parvesh Mehta ProfileResourcesReport error
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