Question 18 The boat's speed in still water is 10km/hr, and the speed of the current is 6km/hr.
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Question 18
The boat's speed in still water is 10km/hr, and the speed of the current is 6km/hr. The boat travels upstream from P to Q and downstream back to P in 8 hours. What is the distance between P and Q?
Show answer & explanation
The total time for a round trip is the sum of the time taken to travel upstream and downstream. By calculating the effective speeds (still water speed minus current for upstream, and plus current for downstream), we can solve for the distance using the formula Time = Distance / Speed.
Step-by-step Derivation:
Step 1: Identify given values.
- Speed of boat in still water (u) = 10 km/hr
- Speed of current (v) = 6 km/hr
- Total time (T) = 8 hours
Step 2: Calculate effective speeds.
- Downstream speed (D) = u + v = 10 + 6 = 16 km/hr
- Upstream speed (U) = u - v = 10 - 6 = 4 km/hr
Step 3: Set up the equation for total time.
Let the distance between P and Q be 'd'.
Total Time = (Time taken upstream) + (Time taken downstream)
8 = (d / 4) + (d / 16)
Step 4: Solve for d.
Find a common denominator for the fractions (which is 16):
8 = (4d / 16) + (d / 16)
8 = 5d / 16
Step 5: Isolate d.
5d = 8 * 16
5d = 128
d = 128 / 5
d = 25.6 km