Question

A motor boat whose speed is 18 km/h 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​

Answer 1

ANSWER-

Given:-

Speed of boat =18km/hr

Distance =24km

Let x be the speed of stream.

Let 'T' and 't' be the time for upstream and downstream.

As we know that,

$time = \frac{distance}{speed}$

For upstream,

Speed =(18−x)km/hr

Distance =24km

Time = T

Therefore,

$T = \frac{24}{18 - x}$

For downstream,

Speed =(18+x)km/hr

Distance =24km

Time =t

Therefore,

$t = \frac{24}{18 + x}$

Now according to the question-

T= t +1

$\frac{24}{18 - x} = \frac{24}{18 + x} + 1$

$\frac{24}{18 - x} - \frac{24}{18 + x} = 1$

$\frac{24(18 + x) - 24(18 - x)}{(18 - x)(18 + x)} = 1$

$(18 - x)(18 + x) = 24(18 + x) - 24(18 - x)$

(18)² - x² = 432 +24 x - 432 +24x

324 - x²= 48x

x² + 48x - 324=0

x²+(54-6)x-324=0

x²+54x-6x-324=0

x(x+54) - 6(x+54)=0

(x+54)(x-6)=0

Either,

x+54=0

x = - 54

Or,

x-6=0

x=6

Since speed cannot be negative.

x is not equal to - 54

∴x=6

Thus the speed of stream is 6km/hr

Hence the correct answer is 6km/hr.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr

Ple ase please make my answer brainliest