BANK & INSURANCE (BOAT AND STREAM) PART 1

Upstream speed = 6 − 2 = 4 km/hr

Let the distance is D

D/4 − D/8 = 4

D/8 = 4

D = 32 km

Boat speed = 9 km/hr

Speed of stream = 9 − 5 = 4 km/hr

Speed of stream is = 12×75/100 = 9 km/hr

Time taken to go 80km = 80/21 = 3.80 hr

Downstream speed = 60/3 = 20

Speed of boat = (20 + 12)/2 = 32/2 = 16 km/hr

Upstream speed = 9

So boat of speed = (15 + 9)/2 = 24/2 = 12 km/hr

Let the speed downstream be “x” km/h, then the speed upstream is “x − 2” km/h.

According to the problem, the time taken to travel downstream is given by:

d/(6 + 2) = d/8 hours

The time taken to travel upstream is given by:

d/(6 − 2) = d/4 hours.

It is given that the time taken to travel upstream is 3 hours more than the time taken to travel downstream.

Therefore,

d/4 − d/8 = 3

Solving for “d”, we get:

d = 24 km.

Speed upstream = (15/2 − x) km/h

Speed downstream = (15/2 + x) km/h

Let the time taken to travel downstream be “t” hours.

Then, the time taken to travel upstream would be “4t” hours.

We know that distance = speed × time.

Therefore, we have:

Distance downstream = (15/2 + x)t

Distance upstream = (15/2 − x)(4t) = (30 − 4x)t

As the distances covered upstream and downstream are the same, we can equate the two equations and solve for “x”:

15/2 + x = (30 − 4x)/4

Multiplying both sides by 4, we get:

30 + 4x = 120 − 16x

20x = 90

x = 4.5 km/h

Therefore, the speed of the stream is 4.5 km/h.

The effective speed of boat A downstream is (16 + x) km/h, and the effective speed of boat B upstream is (14 − x) km/h.

When they travel towards each other, their effective speed is (16 + x) + (14 − x) = 30 km/h.

Let the time taken for them to meet be “t” hours.

Then, the distance covered by boat A is (16 + x)t km, and the distance covered by boat B is (14 − x)t km.

As they are travelling towards each other, the sum of their distances covered will be equal to the distance between them, which is 150 km.

Therefore, we have:

(16 + x)t + (14 − x)t = 150

Simplifying this, we get:

30t = 150

t = 5 hours

Therefore, they will meet after 5 hours

The speed of the boat downstream (i.e., along the direction of the stream) is (25 + 5) = 30 km/h, and the speed of the boat upstream (i.e., against the direction of the stream) is (25 − 5) = 20 km/h.

Let the time taken by the boat to travel downstream be “t1” hours, and the time taken to travel upstream be “t2” hours.

We know that distance = speed × time.

Therefore, we have:

Distance downstream = 30t1 km

Distance upstream = 20t2 km

As the distance covered upstream and downstream is the same, we can equate the two equations and solve for “t1” in terms of “t2”:

30t1 = 20t2

t1 = (2/3)t2

We also know that the total time taken by the boat to travel to the place and come back is 15 hours.

Therefore,

t1 + t2 = 15

Substituting the value of t1 in terms of t2 in the above equation, we get:

(2/3)t2 + t2 = 15

(5/3)t2 = 15

t2 = 9 hours

Substituting this value in the equation for t1, we get:

t1 = (2/3)t2 = 6 hours

Therefore, the distance of the place is:

Distance downstream = 30t1

= 180 km

We know that the speed of the boat downstream (i.e., along the direction of the stream) is (x + y) km/h, and the speed of the boat upstream (i.e., against the direction of the stream) is (x − y) km/h.

Given that the speed downstream is 8 km/h and the speed upstream is 6 km/h.

Therefore, we have:

x + y = 8              (1)

x − y = 6              (2)

Adding equations (1) and (2), we get:

2x = 14

x = 7 km/h

Substituting this value of “x” in equation (1), we get:

y = 1 km/h

Therefore, the speed of the boat in still water is 7 km/h and the speed of the stream is 1 km/h.

To travel a distance of 28 km in still water, the time taken by the boat would be:

Time = Distance / Speed = 28 / 7 = 4 hours