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A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs. Find the speed of the boat in still water and the speed of the water current?
- a)1/2 kmph
- b)7/12 kmph
- c)5 kmph
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs...
Given data:
Distance travelled upstream = 20 km
Time taken upstream = 6 hours
Distance travelled downstream = 18 km
Time taken downstream = 4 hours
Let's assume the speed of the boat in still water as 'x' kmph and the speed of the water current as 'y' kmph.
To find the speed of the boat in still water and the speed of the water current, we will use the formula:
Speed = Distance / Time
Calculations:
Speed upstream = (x - y)
Speed downstream = (x + y)
Using the above formula, we get:
(x - y) = 20 / 6
(x + y) = 18 / 4
Simplifying the above equations, we get:
x - y = 10 / 3
x + y = 9 / 2
Adding the two equations, we get:
2x = (10/3) + (9/2)
2x = (20/6) + (27/6)
2x = 47 / 6
x = 47 / (2 * 6)
x = 47 / 12
Therefore, the speed of the boat in still water is 3.91 kmph.
Substituting the value of x in any of the above equations, we get:
y = (9/2) - (47/12)
y = 7/12
Therefore, the speed of the water current is 0.58 kmph.
Hence, the correct answer is option (b) 7/12 kmph.
Distance travelled upstream = 20 km
Time taken upstream = 6 hours
Distance travelled downstream = 18 km
Time taken downstream = 4 hours
Let's assume the speed of the boat in still water as 'x' kmph and the speed of the water current as 'y' kmph.
To find the speed of the boat in still water and the speed of the water current, we will use the formula:
Speed = Distance / Time
Calculations:
Speed upstream = (x - y)
Speed downstream = (x + y)
Using the above formula, we get:
(x - y) = 20 / 6
(x + y) = 18 / 4
Simplifying the above equations, we get:
x - y = 10 / 3
x + y = 9 / 2
Adding the two equations, we get:
2x = (10/3) + (9/2)
2x = (20/6) + (27/6)
2x = 47 / 6
x = 47 / (2 * 6)
x = 47 / 12
Therefore, the speed of the boat in still water is 3.91 kmph.
Substituting the value of x in any of the above equations, we get:
y = (9/2) - (47/12)
y = 7/12
Therefore, the speed of the water current is 0.58 kmph.
Hence, the correct answer is option (b) 7/12 kmph.
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A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs. Find the speed of the boat in still water and the speed of the water current?a)1/2 kmphb)7/12 kmphc)5 kmphd)none of theseCorrect answer is option 'B'. Can you explain this answer?
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