Login/Sign Up
Home » The boat goes upstream and downstream in hours. In hours, it can go upstream and downstream. Determine the speed of the stream and that of the boat in still water.
The boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water.
CBSE | Class 10 | Exercise 3.10 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
The boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water.

Let’s assume,

The speed of the boat in still water as Ckm/hr

And,

The speed of the stream as Dkm/hr

We know that,

Speed of the boat in upstream =(C-D)km/hr

Speed of the boat in downstream =(C+D)km/hr

So,

Time taken to cover 30 km upstream =30/(C−D)hr [∵ time = distance/ speed]

Time taken to cover 44 km downstream =44/(C+D)hr [∵ time = distance/ speed]

It’s given that the total time of journey is 10 hours. So, this can expressed as

30/(C-D)+44/(C+D)=10 …….. (i)

Similarly,

Time taken to cover 40 km upstream =40/(C-D)hr [∵ time = distance/ speed]

Time taken to cover 55 km downstream =55/(C+D)hr [∵ time = distance/ speed]

And for this case the total time of the journey is given as 13 hours.

Hence, we can write

40/(C-D)+55/(C+D)=13 ……. (ii)

Hence, CD solving (i) and (ii) we get the required solution

Taking, 1/(C-D)=u and 1/(C+D)=v in equations (i) and (ii) we have

30u+44v=10

40u+55v=10

Which can be re- written as,

30u+44v-10=0 ……. (iii)

40u+55v-13=0……… (iv)

Solving these equations CD cross multiplication we get,

\frac{u}{44x-13-55x-10}=\frac{-v}{30x-13-40x-10}=\frac{1}{30\times 55-40\times 44}

u=\frac{-22}{-110}

v=\frac{10}{110}

u=\frac{2}{10}

v=\frac{1}{11}

Now,

1/(C-D)=2/10

=1\times C\times 10=2\left( C-D \right)

⇒ 10=2C-2D

⇒ C-D=5 ……. (v)

And,

1/(C+D)=1/11

⇒ C+D=11 ……. (vi)

Again, solving (v) and (vi)

Adding (v) and (vi), we get

2C=16

⇒ C=8

Using C in (v), we find D

8-D=5

⇒ D=3

Therefore, the speed of the boat in still water is 8km/hr and the speed of the stream is 3km/hr.

i

More Material