# Boats and Streams Quiz Set 004

### Question 1

An airplane can travel at 2 km/h in still air. But it takes thrice as much time to travel upstream as compared to the time it takes downstream, if air is blowing at a rate of R km/h. What is R?

A

1 km/h.

B

2 km/h.

C

3 km/h.

D

\$1{1/3}\$ km/h.

Soln.
Ans: a

If the distance travelled is D, we have \$D/{2/1 - R}\$ = 3 × \$D/{2/1 + R}\$. Cancelling D, and solving for R, we get R = 1 km/h.

### Question 2

An airplane can travel at \$1{5/9}\$ km/h in still air. But it takes thrice as much time to travel upstream as compared to the time it takes downstream, if air is blowing at a rate of R km/h. What is R?

A

\${7/9}\$ km/h.

B

2 km/h.

C

\$2{3/11}\$ km/h.

D

\$3{1/11}\$ km/h.

Soln.
Ans: a

If the distance travelled is D, we have \$D/{14/9 - R}\$ = 3 × \$D/{14/9 + R}\$. Cancelling D, and solving for R, we get R = \${7/9}\$ km/h.

### Question 3

A boat can travel 192 km downstream in 12 hours. If it covers the same distance upstream in 32 hours, what is the rate of flow of the stream?

A

5 kmph.

B

6 kmph.

C

4 kmph.

D

8 kmph.

Soln.
Ans: a

The downstream speed = \$192/12\$ = 16 km/h, and the upstream speed = \$192/32\$ = 6 km/h. By the shortcut method, the speed of the stream is half of the difference between the downstream and upstream speeds of the boat. So the required speed = \${16 - 6}/2\$ = 5 km/h.

### Question 4

The speed of a boat in still water is 16 km/h and rate of flow of the stream is 6 km/h. If it travels upstream for 6 hours, what is the distance travelled by the boat during the journey?

A

60 km.

B

61 km.

C

59 km.

D

63 km.

Soln.
Ans: a

The effective speed of the boat in the stream is 16 - 6 = 10 km/h. The distance is speed × time = 10 × 6 = 60 km.

### Question 5

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. 