6. A child swims in still water at 4.5 km/hr. The river is flowing at a rate of 1.5 km/hr. Find the average speed of the child if he swims same distance upstream and downstream.
a. 3 km/hr
b. 3.5 km/hr
c. 4 km/hr
d. 6 km/hr
∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr
Let distance be D km
7. The time taken by swimmer to swim upstream is 4 hours more than the time he takes to swim downstream. He swims at a speed of 10 km/hr in still water. The stream is flowing gently at 2 km/hr. What is the swimming distance one side?
a. 20 km
b. 72 km
c. 80 km
d. 96 km
X+Y = 10+2 = 12 km/hr and X-Y = 10-2 = 8 km/hr
Let Time be T hours for downstream
Distance is same
∴ D = D
∴ 12 x T = 8 x (T+4)
∴ T = 8 hours = Time for downstream
Distance = 12km/hr x 8 hours = 96 km
8. Practicing for a competition, a swimmer saw that he could swim 20 km downstream in just 1 hr while it took 2 hrs to swim upstream. Find the speed of the river and that of the swimmer respectively.
a. 4 km/hr ; 16 km/hr
b. 5 km/hr ; 15 km/hr
c. 6 km/hr ; 14 km/hr
d. 8 km/hr ; 12 km/hr
X+Y = 20 km/hr and X-Y = 10 km/hr
Adding them we get,
X+Y+X-Y = 30 km/hr
∴ X=15 km/hr = Speed of swimmer in still water
Y=20-15 = 5 km/hr = Speed of river
9. A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that, his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?
a. 2 hours 30 minutes
b. 2 hours 40 minutes
c. 3 hours 10 minutes
d. 4 hours
X+Y = (45+Y) km/hr
∴ Y = 15 km/hr
X-Y = 45-15 = 30 km/hr
10. If Madhuri is asked to swim 24 km along the stream and 36 km against the stream, she will take 6 hrs 30 minutes. While, if the distances upstream and downstream are exchanged, she will take 6 hrs. Find the speed of the stream.
a. 2 km/hr
b. 3 km/hr
c. 4 km/hr
d. 6 km/hr
Similarly in 2nd case,
Multiply equation (1) by 2 and equation (2) by 3 and then subtracting equation (1) from (2)
∴ X+Y = 12 km/hr
∴ X-Y = 8 km/hr
(X+Y) - (X-Y) = 12-8 = 4
∴ Y=2 km/hr = Speed of stream
a. 3 km/hr
b. 3.5 km/hr
c. 4 km/hr
d. 6 km/hr
Answer: c. 4 km/hr
Explanation:
Man's/Boat's Speed = X
Stream/Current/River Speed = Y
∴ Downstream speed = X + Y
Upstream speed = X - Y
∴ X+Y = 4.5+1.5 = 6 km/hr and X-Y = 4.5-1.5 = 3 km/hr
Let distance be D km
| Downstream Time | = | Distance | = | D |
| Speed | 6 |
| Upstream Time | = | D |
| 3 |
| Average Speed | = | Total Distance | = | D+D | = | 6 x 2D | = | 4 km/hr |
| Time taken | D/6+D/3 | 3D |
7. The time taken by swimmer to swim upstream is 4 hours more than the time he takes to swim downstream. He swims at a speed of 10 km/hr in still water. The stream is flowing gently at 2 km/hr. What is the swimming distance one side?
a. 20 km
b. 72 km
c. 80 km
d. 96 km
Answer: d. 96 km
Explanation:
Man's/Boat's Speed = X
Stream/Current/River Speed = Y
∴ Downstream speed = X + Y
Upstream speed = X - Y
X+Y = 10+2 = 12 km/hr and X-Y = 10-2 = 8 km/hr
Let Time be T hours for downstream
Distance is same
∴ D = D
∴ 12 x T = 8 x (T+4)
∴ T = 8 hours = Time for downstream
Distance = 12km/hr x 8 hours = 96 km
8. Practicing for a competition, a swimmer saw that he could swim 20 km downstream in just 1 hr while it took 2 hrs to swim upstream. Find the speed of the river and that of the swimmer respectively.
a. 4 km/hr ; 16 km/hr
b. 5 km/hr ; 15 km/hr
c. 6 km/hr ; 14 km/hr
d. 8 km/hr ; 12 km/hr
Answer: b. 5 km/hr ; 15 km/hr
Explanation:
Man's/Boat's Speed = X
Stream/Current/River Speed = Y
∴ Downstream speed = X + Y
Upstream speed = X - Y
| Downstream Speed | = | Distance covered | = | 20 | = | 20 km/hr |
| Time taken | 1 |
| Upstream Speed | = | 20 | = | 10 km/hr |
| 2 |
Adding them we get,
X+Y+X-Y = 30 km/hr
∴ X=15 km/hr = Speed of swimmer in still water
Y=20-15 = 5 km/hr = Speed of river
9. A fisherman can row his boat to the market for 80 km along the stream. For this he takes 1 hour 20 minutes. His son says that, his father’s rowing speed in still water is 45 km/hr. How much time should he take to row the same distance back, against the stream?
a. 2 hours 30 minutes
b. 2 hours 40 minutes
c. 3 hours 10 minutes
d. 4 hours
Answer: b. 2 hours 40 minutes
Explanation:
Man's/Boat's Speed = X
Stream/Current/River Speed = Y
∴ Downstream speed = X + Y
Upstream speed = X - Y
X+Y = (45+Y) km/hr
| 1 hour 20 minutes = 1 hour | + | 20 | = | 4 | hours |
| 60 | 3 |
| Downstream Speed | = | Distance covered |
| Time taken |
| ∴ 45+Y | = | 80 | = | 60 |
| 4/3 |
X-Y = 45-15 = 30 km/hr
| Time taken to go against the stream | = | 80 | hrs = 2 hours 40 minutes |
| 30 |
10. If Madhuri is asked to swim 24 km along the stream and 36 km against the stream, she will take 6 hrs 30 minutes. While, if the distances upstream and downstream are exchanged, she will take 6 hrs. Find the speed of the stream.
a. 2 km/hr
b. 3 km/hr
c. 4 km/hr
d. 6 km/hr
Answer: a. 2 km/hr
Explanation:
Man's/Boat's Speed = X
Stream/Current/River Speed = Y
∴ Downstream speed = X + Y
Upstream speed = X - Y
| Downstream time | = | Distance | = | 24 |
| speed | X+Y |
| Upstream time | = | Distance | = | 36 |
| speed | X-Y |
| 24 | + | 36 | = 6 ½ hours = | 13 | hours ----------------(1) |
| X+Y | X-Y | 2 |
Similarly in 2nd case,
| 36 | + | 24 | = 6 hours ----------------(2) |
| X+Y | X-Y |
Multiply equation (1) by 2 and equation (2) by 3 and then subtracting equation (1) from (2)
| 3 x 36 | - | 2 x 24 | = 3 x 6 - | 2 x 13 |
| X+Y | X+Y | 2 |
| ∴ | 108 | - | 48 | = 5 |
| X+Y | X+Y |
∴ X+Y = 12 km/hr
| 36 | + | 24 | = 6 -------------Putting value of X+Y in equation (2) |
| 12 | X-Y |
∴ X-Y = 8 km/hr
(X+Y) - (X-Y) = 12-8 = 4
∴ Y=2 km/hr = Speed of stream
