# CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

The speed of a boat in still water is 60 kmph and the speed of the current is 20 kmph. Find the speed downstream and upstream

- (a)
35, 25 kmph

- (b)
40, 60 kmph

- (c)
50, 55 kmph

- (d)
80, 40 kmph

Answer: Option D

**Explanation** :

Speed downstream = 60 + 20 = 80 kmph

Speed upstream = 60 - 20 = 40 kmph

Hence, option (d).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

The speed of a boat in still water is 2 km/h If its speed upstream is 1 km/h, then speed of the stream is :

- (a)
2 kmph

- (b)
3 kmph

- (c)
1 kmph

- (d)
None of these

Answer: Option C

**Explanation** :

Speed of stream = 2 – 1 = 1 km/h

Hence, option (c).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A man can row with the stream at 10 km/h and against the stream at 5 km/h. Man’s speed in still water is :

- (a)
5 kmph

- (b)
2.5 kmph

- (c)
7.5 kmph

- (d)
15 kmph

- (e)
None of these

Answer: Option C

**Explanation** :

Man’s speed in still water = (10 + 5)/2 = 7.5 km/h

Hence, option (c).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boat goes 40 km upstream in 8 hours and a distance of 36 km downstream in 6 hours. The speed of the boat in standing water is :

- (a)
6.5 kmph

- (b)
6 kmph

- (c)
5.5 kmph

- (d)
5 kmph

Answer: Option C

**Explanation** :

Speed upstream = (40 ÷ 8) = 5 km/h

Speed downstream = (36 ÷ 6) = 6 km/h

Speed of boat in standing water = (5 + 6)/2 = 5.5 km/h

Hence, option (c).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 10 hours to row to a place and back. How far is the place?

- (a)
31.2 kmph

- (b)
28.8 kmph

- (c)
30 kmph

- (d)
20 kmph

Answer: Option B

**Explanation** :

Man's speed = 6 km/hr

River’s speed = 1.2 km/hr

Speed while going downstream = (b + r) = (6 + 1.2) = 7.2

Speed while going upstream = (b - r) = (6 - 1.2) = 4.8

(x/7.2) + (x/4.8) = 10

x = 28.8

Hence, option (b).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boatman can row 1 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current

- (a)
1/3 kmph

- (b)
1/6 kmph

- (c)
5/6 kmph

- (d)
None of these

Answer: Option B

**Explanation** :

Speed of the boatman upstream = $\frac{1}{\frac{20}{60}}$ = 3 km/hr.

Speed of the boatman downstream = $\frac{1}{\frac{18}{60}}$ = 10/3 km/hr.

Rate of current = $\frac{downstreamspeed-upstreamspeed}{2}$ = (10/3 - 3)/2 = 1/6 km/hr.

Hence, option (b).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boat travels at a speed of 15 kmph. It travels between points A and B, which are 200 km apart. If the boat goes downstream from A to B in 10 hours, how long will it take to return upstream from B to A (in hours)?

Answer: 20

**Explanation** :

S_{down }= 15 + S_{s}

T = $\frac{D}{{S}_{down}}=\frac{200}{15+{S}_{s}}$

10 = $\frac{200}{15+{S}_{s}}$

15 + S_{s} = 200/10 = 20

S_{s} = 5 kmph

T = $\frac{D}{{S}_{up}}=\frac{200}{15-5}$

Hence, 20.

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

Two boats, travelling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) two minutes before they collide?

- (a)
1/12

- (b)
1/6

- (c)
1/4

- (d)
1/2

Answer: Option D

**Explanation** :

The boats together travel 10 + 5 = 15 km in 60 minutes.

∴ In one minute they can travel 1/4 km

∴ They are 1/2 km apart, two minutes before they collide.

Hence, option (d).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boat can travel 10 km upstream in 2 hours. If the speed of the boat becomes half, then the return journey also takes the same time. What is the speed of water flow?

- (a)
5/3 kmph

- (b)
10/3 kmph

- (c)
7/3 kmph

- (d)
8/3 kmph

- (e)
5/2 kmph

Answer: Option A

**Explanation** :

Let the speed of the boat be Vb and that of the stream be V_{w}.

Now, the time taken by the boat in going upstream = $\frac{10}{{V}_{b}-{V}_{w}}$ = 2

⇒ V_{b} - V_{w} = 5 ... (i)

And the time taken by the boat in going downstream = $\frac{10}{\frac{{V}_{b}}{2}+{V}_{w}}$ = 2

⇒ V_{b}/2 + V_{w} = 5 ... (ii)

Adding (i) and (ii),

(3V_{b})/2 = 10

V_{b }= 20/3

V_{w} = 5 - (10/3) = 5/3 kmph

The speed of the water flow is 5/3 kmph.

Hence, option (a).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boat starts from A and moves towards B. Another boat from B, with the same speed as that of first boat, starts moving towards A. They meet at a point which is 20 km towards B from exactly half-way of A to B and the distance between A and B is 120 km.

What is the ratio of speed of boat to that of water?

- (a)
2 : 1

- (b)
3 : 2

- (c)
3 : 1

- (d)
4 : 1

- (e)
5 : 2

Answer: Option C

**Explanation** :

It is clear that the water flow is from A to B.

Distance travelled by boat starting from A = 80 kms.

Distance travelled by boat starting from B = 40 kms.

Since time travelled is same for both the boats:

$\frac{80}{{V}_{b}+{V}_{w}}=\frac{40}{{V}_{b}-{V}_{w}}$

⇒ V_{b} = 3V_{w}

⇒ V_{b} : V_{w} = 3 : 1

Hence, option (c).

Workspace:

**CRE 4 - Boats and Streams | Arithmetic - Time, Speed & Distance**

A boat P travels 80 km upstream from point A to point B in 10 hours and downstream from point B to point A in 5 hours. Another boat Q can travel from point A to a point C 60 km upstream in 5 hours.

What is the speed of the boat Q in still water?

- (a)
12 kmph

- (b)
16 kmph

- (c)
20 kmph

- (d)
24 kmph

- (e)
30 kmph

Answer: Option B

**Explanation** :

Let P km/hr be the speed of boat P, and Q km/hr be the speed of boat Q.

Let s km/hr be the rate of flow of stream.

We have,

P - s = 80/10 = 8 and P + s = 80/5 = 16

Solving, we get P = 12 and s = 4

Again, Q - s = 60/5 = 12

Thus, s = 4 and Q = 16.

Thus, speed of boat Q in still water is 16 km/hr.

Hence, option (b).

Workspace:

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