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A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
  • a)
    5 : 6
  • b)
    6 : 5
  • c)
    8 : 3
  • d)
    3 : 8
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A boat running upstream takes 8 hours 48 minutes to cover a certain di...
Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

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Most Upvoted Answer
A boat running upstream takes 8 hours 48 minutes to cover a certain di...
Given:
Time taken to cover the distance upstream = 8 hours 48 minutes = 528 minutes
Time taken to cover the distance downstream = 4 hours = 240 minutes

Let the speed of the boat be x km/hr and the speed of the water current be y km/hr.

Formula Used:
Speed = Distance/Time

Calculation:
Let the distance be d km.

When the boat is going upstream,
Speed of boat = x - y
Time taken = 528 minutes = 528/60 hours = 44/5 hours
Distance = d km
Therefore, (x - y) = d/(44/5)

When the boat is going downstream,
Speed of boat = x + y
Time taken = 240 minutes = 4 hours
Distance = d km
Therefore, (x + y) = d/4

We need to find the ratio of x and y.

From the above two equations,
d/(44/5) - d/4 = x - y - x - y
d(1/(44/5) - 1/4) = -2y
d(5/88 - 1/4) = -2y
d(5/88 - 22/88) = -2y
d(-17/88) = -2y
y = d(17/176)

Substituting the value of y in the equation (x + y) = d/4, we get
x + d(17/176) = d/4
x = d/4 - d(17/176)
x = d(22/176) - d(17/176)
x = d(5/176)

Therefore, the ratio of the speed of the boat to the speed of the water current is:

x:y = 5:17/176

Simplifying, we get:
x:y = 5:22/17
x:y = 5:1.294

Rounding off to the nearest integer, we get:
x:y = 5:1

Thus, the answer is option C) 8:3.
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A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?a)5 : 6b)6 : 5c)8 : 3d)3 : 8Correct answer is option 'C'. Can you explain this answer?
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