Question

A man goes 32km upstream and 40 km downstream in 10 hr.Again he goes 38 km upstream and 50 km downstream. then find the speed of the stream? plz solve the question. ​

Answer 1

Step-by-step explanation:

*Given:A man goes 32km upstream and 40 km downstream in 10 hr.Again he goes 38 km upstream and 50 km downstream in 12 hours.

To find: Find the speed of the stream?

Solution:

Let the speed of boat is x km per hour and speed of stream is y km per hour.

Speed of upstream be (x-y)km/h

and speed of stream is (x+y)km/h

Step 1: Make equations from the given condition

Time taken to go 32 km upstream=Distance /speed

=32/x-y hours

Time taken to go 40 km downstream=Distance /speed

=40/x+y hours

Total time taken during the journey is 10 hours

Thus,

$\bold{ \frac{32}{x - y} + \frac{40}{x + y} = 10} \: \: \: ...eq1$

Time taken to go 38 km upstream=Distance /speed

=38/x-y

Time taken to go 50 km downstream=Distance /speed

=50/x+y

Total time taken during the journey is 12 hours

Thus,

$\bold{ \frac{38}{x - y} + \frac{50}{x + y} = 12} \: \: \: ...eq2$

Step 2:Convert these equations in linear equations in two variables

Solve eq1 and eq2

Let

$\frac{1}{x - y} = a \\ \\ \frac{1}{x + y} = b$

thus

$32a + 40b = 10 \\ or \\ 16a + 20b = 5 \: \: \:... eq3\\ \\ 38a + 50b = 12 \\ or \\ 19a + 25b = 6 \: \: \:...eq4$

Solution of eq3 and eq4 gives value of a and b.

multiply eq3 by 25 and eq4 by 20 and subtract both

$400a + 500b = 125\\ 380a + 500b = 120 \\ - - - - - - - - - \\ 20a = 5\\ \\ a = \frac{5}{20} \\ \\ a = \frac{1}{4}$

put the value of a in eq3

$16 \times \frac{1}{4} + 20b = 5 \\ \\ 4+ 20b = 5 \\ \\ 20b = 1 \\ \\ b = \frac{ 1}{20}$

Step 3: Find values of x and y.

Put these values of a and b in assumption

$\frac{1}{x - y} = \frac{1}{4} \\ \\ x - y = 4 \: \: \: ...eq5\\ \\ \frac{1}{x + y} = \frac{ 1}{20} \\ \\ x + y = 20 \: \: \: ...eq6$

add both equations 5 and 6

$x - y = 4\\ x + y =20 \\ - - - - - - - - - \\ 2x = 24 \\ \\ x = \frac{24}{2} \\ \\ \bold{\boxed{x = 12}}$

put value of x in eq5

$x - y = 4 \\ 12 - y = 4 \\ \\ - y = 4 - 12 \\ \\ - y = - 8 \\ \\ \bold{\boxed{y = 8}}$

Final answer:

Speed of stream is 8 km/hour.

*Note: Question is incomplete.It was assumed that he goes 38 km upstream and 50 km downstream in 12 hours.

Hope it helps you.

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