# Boats and Streams Quiz Set 008

### Question 1

A boat has a speed of 8 km/h in a still stream. What is the speed downstream in a stream that is flowing at a speed of 6 km/h?

A

14 kmph.

B

15 kmph.

C

13 kmph.

D

17 kmph.

Soln.
Ans: a

The downstream speed is the speed along the direction of the flow of the stream. It is equal to the sum of the speed of the boat in still water and the speed of the stream. So the speed downstream is 8 + 6 = 14 km/h.

### Question 2

A man can row a boat at the rate of 14 km/h in still water, and at the rate of 8 km/h against the stream. At what rate can he row down the stream?

A

20 km/h.

B

21 km/h.

C

19 km/h.

D

23 km/h.

Soln.
Ans: a

If v is the speed of the stream, 14 - v = 8, so the speed of the stream is 14 - 8 = 6 km/h. So his downstream speed would be 14 + 6 = 20 km/h.

### Question 3

The speed of a boat in still water is 16 km/h and rate of flow of the stream is 8 km/h. If it travels upstream for 7 hours, what is the distance travelled by the boat during the journey?

A

56 km.

B

57 km.

C

55 km.

D

59 km.

Soln.
Ans: a

The effective speed of the boat in the stream is 16 - 8 = 8 km/h. The distance is speed × time = 8 × 7 = 56 km.

### Question 4

The upstream journey of a boat takes 8 times the time it takes it to complete the downstream journey. What is the ratio of the speed of the boat in still water to the speed of the stream?

A

\$1{2/7}\$.

B

\$2{2/3}\$.

C

\${2/9}\$.

D

\$3{1/3}\$.

Soln.
Ans: a

Let the distance be L and the speed of the boat in still water be u, with v being the speed of the stream. We are given \$L/{u - v} = 8 × L/{u + v}\$. We can solve this equation for u/v to get u/v = \${8 + 1}/{8 - 1}\$ = \$1{2/7}\$.

### Question 5

A boat has a downstream speed of 16 km/h and an upstream speed of 12 km/h. What is the speed of the boat in still water?

A

14 kmph.

B

15 kmph.

C

13 kmph.

D

17 kmph.

Soln.
Ans: a

By the shortcut method, the speed of the boat in still water is average of downstream and upstream speeds. So the required speed = \${16 + 12}/2\$ = 14 km/h.