Question

a motor boat whose speed is 15 km/hr in still water, goes 30km down stream and comes back in total time of 4hrs 30 mins find the speed of the stream

Answer 1

Answer:

5km/hr

Step-by-step explanation:

It is given that speed of motor boat in still water is 15 km/hr and total distance travelled is 30 km.

Let the speed of the stream be x km/hr then the speed upstream is (15−x) km/hr and speed downstream is (15+x) km/hr.

It is also given that total time taken is 4 hours 30 minutes, therefore,

Time taken to row down the stream is

$\tt \: \frac{30}{15 + x} and$

Time taken to row up the stream is

$\tt \: \frac{30}{15 - x}$

Thus, we have

$\longrightarrow \tt \: \frac{30}{15 + x} + \frac{30}{15 - x} = \frac{9}{2} \\ \longrightarrow \tt \frac{30(15 - x) + 30(15 + x)}{(15 - x)(15 + x)} = \frac{9}{2} \\ \longrightarrow \tt \frac{450 - 30x + 450 + 30x}{ {(15)}^{2} - {x}^{2} } = \frac{9}{2} \\ \longrightarrow \tt \: \frac{900}{225 - {x}^{2} } = \frac{9}{2} \\ \longrightarrow \tt2 \times 900 = 9(225 - {x}^{2} \\ \longrightarrow \tt1800 = 9(225 - {x}^{2} ) \\ \longrightarrow \tt225 - {x}^{2} = \frac{ \cancel{1800}}{ \cancel{9}} \\\longrightarrow \tt 225 - {x}^{2} = 200 \\ \longrightarrow \tt - {x}^{2} = 200 - 225 \\ \longrightarrow \tt - {x}^{2} = - 25 \\ \longrightarrow \tt {x }^{2} = 25 \\ \longrightarrow \tt \: x = \blue{5}$

Since the speed cannot be negative thus, x=5.

Hence, the speed of the stream is 5 km/hr.