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A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?
- a)115 km
- b)120 km
- c)140 km
- d)165 km
- e)150 km
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A boat takes 28 hours for travelling downstream from point A to point ...
Downstream speed = 9+6 = 15
Upstream speed = 9-6 = 3
Now total time is 28 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/3 = 28
Solve, d = 120 km
Upstream speed = 9-6 = 3
Now total time is 28 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/3 = 28
Solve, d = 120 km
Most Upvoted Answer
A boat takes 28 hours for travelling downstream from point A to point ...
Problem: A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?
Solution:
Let the distance between A and B be x km.
Let the speed of the boat downstream be y km/hr. Then,
Speed downstream = (Speed of boat in still water) + (Speed of stream)
y = 9 + 6 = 15 km/hr
Let the speed of the boat upstream be z km/hr. Then,
Speed upstream = (Speed of boat in still water) - (Speed of stream)
z = 9 - 6 = 3 km/hr
Let t1 and t2 be the time taken by the boat to travel downstream from A to B and upstream from B to C respectively.
t1 = x/(y+6) and t2 = x/(z+6)
As per the problem,
t1 + t2 = 28 hours
x/(y+6) + x/(z+6) = 28
x(2y+2z+12)/(y+6)(z+6) = 28
x(2(15+3)+12)/(15+6)(3+6) = 28
x = 120 km
Therefore, the distance between A and B is 120 km.
Answer: Option B) 120 km
Solution:
Let the distance between A and B be x km.
Let the speed of the boat downstream be y km/hr. Then,
Speed downstream = (Speed of boat in still water) + (Speed of stream)
y = 9 + 6 = 15 km/hr
Let the speed of the boat upstream be z km/hr. Then,
Speed upstream = (Speed of boat in still water) - (Speed of stream)
z = 9 - 6 = 3 km/hr
Let t1 and t2 be the time taken by the boat to travel downstream from A to B and upstream from B to C respectively.
t1 = x/(y+6) and t2 = x/(z+6)
As per the problem,
t1 + t2 = 28 hours
x/(y+6) + x/(z+6) = 28
x(2y+2z+12)/(y+6)(z+6) = 28
x(2(15+3)+12)/(15+6)(3+6) = 28
x = 120 km
Therefore, the distance between A and B is 120 km.
Answer: Option B) 120 km
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Community Answer
A boat takes 28 hours for travelling downstream from point A to point ...
Downstream speed = 9+6 = 15
Upstream speed = 9-6 = 3
Now total time is 28 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/3 = 28
Solve, d = 120 km
Upstream speed = 9-6 = 3
Now total time is 28 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/3 = 28
Solve, d = 120 km
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