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 relative speeds (boat speed minus current for upstream, and boat speed plus current for downstream), we can set up an algebraic equation to solve for the distance.
Step-by-step Derivation:
Step 1: Identify given values.
Boat speed in still water (v) = 10 km/hr
Speed of current (c) = 6 km/hr
Total time (T) = 8 hours
Let the distance between P and Q be 'd'.
Step 2: Calculate relative speeds.
Downstream speed (v + c) = 10 + 6 = 16 km/hr
Upstream speed (v - c) = 10 - 6 = 4 km/hr
Step 3: Set up the time equation.
Time = Distance / Speed
Time taken for upstream + Time taken for downstream = Total Time
(d / 4) + (d / 16) = 8
Step 4: Solve for d.
Find a common denominator for the fractions (which is 16):
(4d / 16) + (d / 16) = 8
(5d / 16) = 8
5d = 8 * 16
5d = 128
d = 128 / 5
d = 25.6 km