Question

The speed of a boat in still water is 15 km/hr. It can go 45km upstream and return downstream to the original point in 6 hours and 45 min . Find the speed of the stream.

Answer 1

$\textbf{Answer:}$

Let the speed of stream be x

Speed of the boat in still water = 15 km/hr

Speed of boat against stream = (15 - a) km/hr

Speed of the boat with stream = (15 + a)km/hr

Given that, boat goes 45 km upstream and returns in 6 hr 50 min.

Time taken cover to cover 45 km against the stream = (45 / 15 - a) hr

Time taken to cover with the stream
= (45 / 15 + a) hr

Both these equations are equal to 6 hrs 45 mins...

6 + 3 / 4 = 27 / 4

We get it as ↓

$( \frac{45}{15 - a} )( \frac{45}{15 + a} ) = \frac{27}{4}$

Now, taking LCM = 4(15 - a)(15 + a)

$\frac{45}{15 - a} .4(15 - a)(15 + a) + \frac{45}{15 + a}. 4(15 - a)(15 + a)$

$= 27(15 - a)(15 + a)$

➠ 45×4(15 + a) + 45×4(15 - a) = 27(15 - a)(15 +a)

➠ 180(15 + a) + 180(15 - a) = 27(15 - a)(15 + a)

➠ 180a + 2700 + 2700 - 180a = 27(225 - a²)

➠ 5400 = 6075 - 27a²

➠ - 27a² = -675

➠ a² = 675 / 27

➠ a² = 25

➠ a = 5

Therefore, the speed of stream = $\textbf{5 km/hr}$
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Answer 2

A Formula,

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

Solution :

Let the speed of stream be x km/hr,

Given, Speed of boat when going to upstream = ( 15 - x ) km/hr

=> 45 / time = ( 15 - x )

=> 45 / ( 15 - x )minutes

When, going downstream, speed of boat = ( 15 + x ) km/hr

=> 45 / time = 15 + x

=> 45 / ( 15 + x ) = time

Total time = 6 hr 45 minutes
Total time = 6 hr + ( 45 × 1/60 ) hr
Total time = ( 6 + 3/4 ) hr
Total time = 27/4 hr

$\frac{45}{15 - x} + \frac{45}{15 + x} = \frac{27}{4} \\ \\ \\ => \frac{5}{15 - x} + \frac{5}{15 + x} = \frac{3}{4} \\ \\ \\ => \frac{75 + 5x + 75 - 5x}{(15 - x)(15 + x)} = \frac{3}{4} \\ \\ \\ => 600 = 675 - 3 {x}^{2} \\ \\ \\ => 3 {x}^{2} = 75 \\ \\ \\ = > {x}^{2} = \frac{75}{3} \\ \\ \\ {x}^{2} = 25$

x = 5

Hence, speed of stream = 5 km/hr