# Boats and Streams Quiz Set 009

### Question 1

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 28. What is the product of the speed of the stream and that of the boat in still water?

A

7.

B

8.

C

6.

D

10.

Soln.
Ans: a

Let the speed of the boat in still water be u, and let v be the speed of the stream. The difference of squares of the speeds is \$(u + v)^2 - (u - v)^2\$, which is \$u^2 + v^2 + 2uv - (u^2 + v^2 - 2uv)\$ = 4uv = 28. We get uv = \$28/4\$ = 7.

### Question 2

The speed of a boat in still water is 56 km/h. It takes the same time to travel an upstream distance of 11 km as it takes to travel a downstream distance of 17 km. The rate of flow of the stream is?

A

12 km/h.

B

13 km/h.

C

11 km/h.

D

15 km/h.

Soln.
Ans: a

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So \$11/{56 - v}\$ = \$17/{56 + v}\$. Solving for v, or verifying by putting the given options one by one, we get v = 12 km/h.

### Question 3

The difference of the squares of the downstream and upstream speeds of a boat in a stream is 12. What is the product of the speed of the stream and that of the boat in still water?

A

3.

B

4.

C

2.

D

6.

Soln.
Ans: a

Let the speed of the boat in still water be u, and let v be the speed of the stream. The difference of squares of the speeds is \$(u + v)^2 - (u - v)^2\$, which is \$u^2 + v^2 + 2uv - (u^2 + v^2 - 2uv)\$ = 4uv = 12. We get uv = \$12/4\$ = 3.

### Question 4

A man can row a boat at the rate of 14 km/h in still water, and at the rate of 4 km/h against the stream. At what rate can he row down the stream?

A

24 km/h.

B

25 km/h.

C

23 km/h.

D

27 km/h.

Soln.
Ans: a

If v is the speed of the stream, 14 - v = 4, so the speed of the stream is 14 - 4 = 10 km/h. So his downstream speed would be 14 + 10 = 24 km/h.

### Question 5

The speed of an aircraft in still air is 14 km/h and rate of wind is 8 km/h. If it travels along the direction of the wind for 7 hours, what is the distance travelled by the aircraft during the journey?

A

154 km.

B

155 km.

C

153 km.

D

157 km.

Soln.
Ans: a

The effective speed of the aircraft in the air is 14 + 8 = 22 km/h. The distance is speed × time = 22 × 7 = 154 km. 