Boats and Streams
- Speed of motorboat in still water is 45 km/h. If the motor travels 80 km along the stream in 1 h 20 min, then the time taken by it to cover the same distance against the stream will be ?
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Let speed of stream be x km/h
Given speed of motorboat in still water = 45 km/h
∴ Speed of boat along stream = (45 + x) km/h
According to the question,
45 + x = 80 x 11/3Correct Option: C
Let speed of stream be x km/h
Given speed of motorboat in still water = 45 km/h
∴ Speed of boat along stream = (45 + x) km/h
According to the question,
45 + x = 80 x 11/3
⇒ 45 + x = 80 x 3 / 4
⇒ x = 60 - 45 = 15
⇒ Speed of boat against stream = 45 - 15 = 30 km/h
Hence, required time = Distance / Speed = 80 / 30
= (8 x 60)/3 = 160 min
= 2 h 40 min
- The speed of a boat in still water is 4 km/hr and the speed of current is 2 km/hr. If the time taken to reach a certain distance upstream is 9 hours, find the time it will take to go same distance downstream ?
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Upstream distance = (4 - 2) x 9 = 18 km
Correct Option: D
Upstream distance = (4 - 2) x 9 = 18 km
∴ Required time = 18/(4 + 2) = 3 hrs.
- A motorboat travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the stream is ?
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Let the speed of a boat and stream be U and V km/h
∴ Speed of boat along stream = (U + V) km/h
and speed of boat against stream = (U - V) km/h
According to the question,
25/(U - V) + 39/(U + V) = 8 ....(i)
and 35/(U - V) + 52/(U + V ) = 11 ..(ii)Correct Option: C
Let the speed of a boat and stream be U and V km/h
∴ Speed of boat along stream = (U + V) km/h
and speed of boat against stream = (U - V) km/h
According to the question,
25/(U - V) + 39/(U + V) = 8 ....(i)
and 35/(U - V) + 52/(U + V ) = 11 ..(ii)
On multiplying Eq. (i) by 4 and Eq. (ii) by 3, then subtract Eq. (ii) from Eq, we get
100/(U - V) - 105/(U - V) = -1
⇒ 5/(U - V) = 1
⇒ U - V = 5 ...(iii)
On substituting the value of (U - V) = 5 in Eq. (i) we get
25/5 + 39/(U + V) = 8
⇒ 39/(U + V) = 8 - 5
⇒ U + V = 39/3
⇒ U + V = 13 ....(iv)
On solving Eqs. (iii) and (iv), we get
U = 9 and V = 4
Hence, speed of stream = 4 km/h
- A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the water current, respectively ?
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Let boat's rate upstream be U and boat's rate downstream = V
According to the question.
Distance covered in 528 min = Distance covered in 240 min
⇒ Distance covered in 8 h 48 min = Distance covered in 4 h
⇒ U x 84/5 = V x 4
⇒ (44 x U)/5 = 4V
⇒ V = (11 x U)/5
∴ Required ratio = (V + U)/2 : (V - U)/2Correct Option: C
Let boat's rate upstream be U and boat's rate downstream = V
According to the question.
Distance covered in 528 min = Distance covered in 240 min
⇒ Distance covered in 8 h 48 min = Distance covered in 4 h
⇒ U x 84/5 = V x 4
⇒ (44 x U)/5 = 4V
⇒ V = (11 x U)/5
∴ Required ratio = (V + U)/2 : (V - U)/2
⇒ = (11U/5 + U)/2 : (11U/5 - U)/ 2
⇒ = 16U/5 : 6U/5 = 8 : 3
- A man can row against the current three-fourth of a kilometre in 15 min and returns same distance in 10 min, then ratio of his speed to that of current is ?
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Let the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
⇒ U - V = 3 ......(i)
and (3/4) x (60/10) = U + V
⇒ U + V = 9/2 ...(ii)Correct Option: D
Let the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
⇒ U - V = 3 ......(i)
and (3/4) x (60/10) = U + V
⇒ U + V = 9/2 ...(ii)
On adding Eqs. (i) and (ii), we get
2U = 3 + 9/2
⇒ U = 15/4
On putting the value of U in Eq. (ii), we get
15/4 + V = 9/2
V = 9/2 - 15/4 = 18 - 15/4
⇒ V = 3/4
Hence, speed of man U = 15/4 and
Speed of current V = 3/4
Hence, required ratio = 15/4 : 3/4 = 5 : 1
