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A boat takes 50% more time to cover a certain distance upstream than that downstream. Find the speed of boat, if speed of water is 5 kmph.
- a)15 km/hr
- b)25 km/hr
- c)20 km/hr
- d)10 km/hr
Correct answer is option 'B'. Can you explain this answer?
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To solve this problem, we can use the concept of relative speed.
Let's assume the speed of the boat in still water is x km/hr.
Speed of the boat downstream = (x + 5) km/hr
Speed of the boat upstream = (x - 5) km/hr
Given that the boat takes 50% more time to cover the distance upstream than downstream.
The time taken to cover the distance downstream is t hours.
The time taken to cover the distance upstream is 1.5t hours (50% more than t).
We know that distance = speed × time.
Therefore, the distance downstream is (x + 5) × t km.
The distance upstream is (x - 5) × 1.5t km.
Since the distance covered upstream and downstream is the same, we can set up the equation:
(x + 5) × t = (x - 5) × 1.5t
Simplifying this equation, we get:
xt + 5t = 1.5xt - 7.5t
xt - 1.5xt = -5t - 7.5t
-0.5xt = -12.5t
Dividing both sides of the equation by -12.5t, we get:
-0.5x = -12.5
Simplifying further, we find:
x = -12.5 / -0.5
x = 25
Therefore, the speed of the boat in still water is 25 km/hr.
Hence, the correct answer is option B) 25 km/hr.
Let's assume the speed of the boat in still water is x km/hr.
Speed of the boat downstream = (x + 5) km/hr
Speed of the boat upstream = (x - 5) km/hr
Given that the boat takes 50% more time to cover the distance upstream than downstream.
The time taken to cover the distance downstream is t hours.
The time taken to cover the distance upstream is 1.5t hours (50% more than t).
We know that distance = speed × time.
Therefore, the distance downstream is (x + 5) × t km.
The distance upstream is (x - 5) × 1.5t km.
Since the distance covered upstream and downstream is the same, we can set up the equation:
(x + 5) × t = (x - 5) × 1.5t
Simplifying this equation, we get:
xt + 5t = 1.5xt - 7.5t
xt - 1.5xt = -5t - 7.5t
-0.5xt = -12.5t
Dividing both sides of the equation by -12.5t, we get:
-0.5x = -12.5
Simplifying further, we find:
x = -12.5 / -0.5
x = 25
Therefore, the speed of the boat in still water is 25 km/hr.
Hence, the correct answer is option B) 25 km/hr.
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A boat takes 50% more time to cover a certain distance upstream than that downstream. Find the speed of boat, if speed of water is 5 kmph.a)15 km/hrb)25 km/hrc)20 km/hrd)10 km/hrCorrect answer is option 'B'. Can you explain this answer?
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