Question

A motor boat can travel 30 km upstream and23 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed off the stream.

Answer 1

We know that Speed = Distance / Time. This means Time = Distance / Speed

Let "u" be speed upstream and "d" be speed downstream

Using this we get:
30/u + 23/d = 7 ------------- (i)

We are also given that the boat can travel up and down in 5 hours. This means:
21/u + 21/d = 5 ------------- (ii)

Multiplying (ii) by 30/21, we get
30/u + 30/d = 50/7 --------- (iii)

Subtracting (iii) from (i), we get:
d = 49 km/hr

Inputting this in equation (i), we get u = 4.59km/hr

We know that Speed Upstream = Speed of boat - Speed of stream
and Speed Downstream = Speed of boat - Speed of stream

From here we get two more equations:
u = Sb - Sr, this means: 4.59 = Sb - Sr ----------- (iv)
and
d = Sb+Sr, this means: 49 = Sb + Sr ------------- (v)

Adding (iv) and (v), we get:
Sb = 26.795 km/hr; substituting this value in equation (iv) we get
Sr = 22.205 km/hr

Please note, Sb = Speed of boat in still water and Sr = speed of stream.

Answer 2

Answer:

Step-by-step explanation:

Let speed of water=x km/h

''. ". ". Boat=y km/h

Speed of upstream=x-y km/ h

Downstream=x+y km/ h

A.T.1st condition

30/x-y + 28/x+y = 7

30a+28b=7___eq.1. (Where x-y= a,x+y=b)

A.T.2nd condition

21/x-y +21/x+y =5

21a+21b=5

Multiply 21 in eq.1 and 30 in eq.2 both sides

Apply elimination method or as per ur choice

We get,b=1/14

a=1/6

x-y=6___eq.3

x+y=14___ eq.4

Solve these eq. By any method and v get our ans as x=10 and y=4