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/plus current speed) and using the distance formula, we can solve for the distance between P and Q.
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 Upstream + Time 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