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A boat takes same time to travel 40 km upstream and 60 km downstream. If the speed of the stream is 15 km/hr then find the time taken by the boat in one side.
- a)2/3 hr
- b)3/2 hr
- c)1/3 hr
- d)4/9 hr
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A boat takes same time to travel 40 km upstream and 60 km downstream. ...
GIVEN:
A boat takes same time to travel 40 km upstream and 60 km downstream.
Speed of the stream = 15 km/hr
FORMULA USED:
Time = Distance / Speed
CALCULATION:
Let speed of boat in still water be M kmph.
Given,
Speed downstream = M + 15
Speed upstream = M – 15
Then,
⇒ 60/(M + 15) = 40/(M – 15)
⇒ 60M – 900 = 40M + 600
⇒ 20M = 1500
⇒ M = 75
Speed of boat in still water is 75 kmph.
Downstream speed = 75 + 15 = 90 kmph
Time taken = 60/90 = 2/3 hr.
Most Upvoted Answer
A boat takes same time to travel 40 km upstream and 60 km downstream. ...
Given:
- Speed of the stream = 15 km/hr
- Distance traveled upstream = 40 km
- Distance traveled downstream = 60 km
To find:
- Time taken by the boat in one side
Approach:
We can solve this problem by using the formula:
Time = Distance / Speed
We need to find the time taken by the boat to travel 40 km upstream and 60 km downstream. Since the boat is traveling in opposite directions, the speed of the boat will be the difference between the speed of the boat in still water and the speed of the stream.
Let's assume the speed of the boat in still water is 'x' km/hr.
1. Time taken to travel upstream:
The speed of the boat relative to the ground while traveling upstream is (x - 15) km/hr. Using the formula,
Time taken to travel upstream = Distance / Speed
Time taken to travel upstream = 40 / (x - 15) hours
2. Time taken to travel downstream:
The speed of the boat relative to the ground while traveling downstream is (x + 15) km/hr. Using the formula,
Time taken to travel downstream = Distance / Speed
Time taken to travel downstream = 60 / (x + 15) hours
According to the given condition, the time taken to travel upstream is equal to the time taken to travel downstream. So,
40 / (x - 15) = 60 / (x + 15)
Now, we can solve this equation to find the value of 'x'.
Cross-multiplying the equation:
40(x + 15) = 60(x - 15)
40x + 600 = 60x - 900
20x = 1500
x = 75
Time taken by the boat in one side:
Now, we can substitute the value of 'x' in either of the equations to find the time.
Time taken to travel upstream = 40 / (x - 15)
Time taken to travel upstream = 40 / (75 - 15)
Time taken to travel upstream = 40 / 60
Time taken to travel upstream = 2/3 hour
Therefore, the time taken by the boat in one side is 2/3 hour, which corresponds to option A.
- Speed of the stream = 15 km/hr
- Distance traveled upstream = 40 km
- Distance traveled downstream = 60 km
To find:
- Time taken by the boat in one side
Approach:
We can solve this problem by using the formula:
Time = Distance / Speed
We need to find the time taken by the boat to travel 40 km upstream and 60 km downstream. Since the boat is traveling in opposite directions, the speed of the boat will be the difference between the speed of the boat in still water and the speed of the stream.
Let's assume the speed of the boat in still water is 'x' km/hr.
1. Time taken to travel upstream:
The speed of the boat relative to the ground while traveling upstream is (x - 15) km/hr. Using the formula,
Time taken to travel upstream = Distance / Speed
Time taken to travel upstream = 40 / (x - 15) hours
2. Time taken to travel downstream:
The speed of the boat relative to the ground while traveling downstream is (x + 15) km/hr. Using the formula,
Time taken to travel downstream = Distance / Speed
Time taken to travel downstream = 60 / (x + 15) hours
According to the given condition, the time taken to travel upstream is equal to the time taken to travel downstream. So,
40 / (x - 15) = 60 / (x + 15)
Now, we can solve this equation to find the value of 'x'.
Cross-multiplying the equation:
40(x + 15) = 60(x - 15)
40x + 600 = 60x - 900
20x = 1500
x = 75
Time taken by the boat in one side:
Now, we can substitute the value of 'x' in either of the equations to find the time.
Time taken to travel upstream = 40 / (x - 15)
Time taken to travel upstream = 40 / (75 - 15)
Time taken to travel upstream = 40 / 60
Time taken to travel upstream = 2/3 hour
Therefore, the time taken by the boat in one side is 2/3 hour, which corresponds to option A.
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