Question

solve the word problem​

Answer 1

Question :

The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.

Answer:

The speed of the stream is 5 km/h

Solution :

Let the speed of stream be x km/hr.

So,

upstream = 15 -x.

downstream = 15 +x.

We know,

Distance = Speed * Times.

$\: \: \boxed{ \tt \: d = s \times t.}$

$\leadsto \tt 30 = (15 - x) \times t \\</p><p>\leadsto \tt \frac{ 30}{(15 - x)} = t.$

And,

$\leadsto \tt30 = (15 + x) \times t. \\ \leadsto \tt \frac{ 30}{ (15 + x) }= t.$

According to Question,our equation become

$\: \: \tt \frac{30}{15 + x} + \frac{30}{15 - x} = 4 \times \frac{30}{60} \\</p><p>\leadsto \tt \frac{30}{15 + x} + \frac{30}{15 - x} = \frac{9}{2} \\</p><p>\leadsto \tt \frac{30(15 - x) + (15 + x)30}{{15 }^{2} - {x}^{2} } = \frac{9}{2} \\</p><p>\leadsto \tt \frac{450 - 30x + 450 + 30x}{225 - {x}^{2} } = \frac{9}{2} \\</p><p>\leadsto \tt \frac{450 \cancel{- 30x} + 450 + \cancel{30x}}{225 - {x}^{2} } = \frac{9}{2} \\</p><p>\leadsto \tt \cancel{1800} = \cancel9(225 - {x}^{2} ) \\</p><p>\leadsto \tt 200 = 225 - {x}^{2} \\ \leadsto \tt25 = {x}^{2} \\</p><p>\leadsto \tt x = \pm5.$

Speed never be negative so,take x= 5 km/h.

Therefore,the speed of the stream be 5 km/h.