A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. The speed of the stream is
Approved Tutor Answer11 Months agoTo find the speed of the stream, we can use the information given about the motorboat's journey upstream and downstream. Let's break it down step by step.
Let the speed of the stream be x km/hr.
The effective speed of the boat upstream is (18 - x) km/hr, and downstream it is (18 + x) km/hr.
The time taken to travel upstream is:
Time upstream = Distance / Speed = 24 / (18 - x)
The time taken to travel downstream is:
Time downstream = Distance / Speed = 24 / (18 + x)
According to the problem, the time taken upstream is 1 hour more than the time taken downstream:
24 / (18 - x) = 24 / (18 + x) + 1
To solve for x, we can cross-multiply and simplify:
Using the quadratic formula x = [-b ± √(b² - 4ac)] / 2a, where a = 1, b = 48, and c = -324:
x = [-48 ± √(48² + 4 × 324)] / 2
Calculating this gives us two potential solutions for x.
After solving, we find that the speed of the stream is 6 km/hr.
The speed of the stream is A. 6 km/hr.
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