A motor boar whose speed is $18 k m / h r$ in still water takes $1 h r$ more to go $24 k m$ upstream then to return downstream to the same spot. Find the speed of the stream.

Open in App

Solution

Given speed of boat in still water = 18 km/hr
Let speed of stream be x km/hr
Speed of boat upstream = speed of boat in still water - speed of stream
= (18-x) km/hr
speed of boat downstream = (18+x) km/hr
Time of upstream journey = Time of downstream journey + 1 hr
$\frac{D i s t a n c e c o v e r e d b y u p s t r e a m}{s p e e d o f b o a t u p s t r e a m} = \frac{D i s t a n c e c o v e r e d d o w n}{s p e e d o f b o a t d o w n} = + 1 h r$
$\frac{24 k m}{(18 - x) k m / h r} = \frac{24 k m}{(18 + x) k m / h r} + 1 h r$
$\frac{24}{18 - x} - \frac{24}{18 + x} = 1 h r$
$\frac{432 + 24 x - 432 + 24 x}{(18 - x) (18 + x)} = 1$
$48 x = 18^{2} - x^{2}$
$x^{2} + 48 x - 324 = 0$
$x^{2} + 54 x - 6 x - 324 = 0$
$x (x + 54) - 6 (x + 54) = 0$
$(x + 54) (x - 6) = 0$
$x = - 54$ or $x = 6$
speed cannot be negative
so $x = 6$

Suggest Corrections

Similar questions

Q. A motor boat whose speed is

18 k m / h

in still water takes

1

hr more to go

24 k m

, upstream than to return downstream to the same spot. Find the speed of the stream.

A motor boat whose speed in still water is 18 km /hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

Q. A motor boat whose speed is

24 k m / h

in still water takes

1 h o u r

more to go

32 k m

upstream than to return downstream to the same spot. Find the speed of the stream.

A motor boat whose speed is 18 $\frac{k m}{h r}$ in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.

Q. A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream that to return down stream to the same spot. Find the speed of the stream.

Join BYJU'S Learning Program

A motor boar whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream then to return downstream to the same spot. Find the speed of the stream.

A motor boar whose speed is $18 k m / h r$ in still water takes $1 h r$ more to go $24 k m$ upstream then to return downstream to the same spot. Find the speed of the stream.