Question

A boat goes 25km upstream and 35km downstream in 10 hours. In 15 hours, it can go 40 km upstream and 49km downstream. Determine the speed of the stream and that of boat in still water​

Answer 1

Answer:

Speed of the stream is 1 km/h and speed of boat is 6 km/h

Step-by-step explanation:

Let spped of water is x km/h and speed of stream is y km/h.

Then, speed at upstream =x−y km/h

Speed at downstream =x+y km/h

Case -1 : 25x−y+35x+y=10

⇒5x−y+7x+y=2→(1)

Case-2 : 40x−y+49x+y=15→(2)

Let 1x−y=a,1x+y=b

So, the equation (1) and (2) becomes,

5a+7b=2→(3)

40a+49b=15→(4)

Now, multiplying (3) with 7 and subtracting it from (4),

⇒40a+49b−35a−49b=15−14

⇒5a=1

⇒a=15

Putting value of a in (3),

⇒5(15)+7b=2

⇒b=17

∴x−y=5andx+y=7

⇒x−y+x+y=5+7

⇒2x=12⇒x=6

⇒y=7−6=1

∴ Speed of the stream is 1 km/h and speed of boat is 6 km/h.

Answer 2

The speed of the stream is 1 kmph and the speed of the boat in still water is 6 kmph.

Given:

• A boat goes 25km upstream and 35km downstream in 10 hours.
• In 15 hours, it can go 40 km upstream and 49km downstream.

To find:

• Determine the speed of the stream and that of boat in still water.

Solution:

Concept/Formula to be used:

Let the speed of boat in still water is 'x' kmph and speed of stream is 'y' kmph.

• Speed= Distance/Time
• Speed of boat upstream: (x-y) kmph
• Speed of boat downstream:(x+y) kmph

Step 1:

Write the equations.

ATQ,

A boat goes 25km upstream and 35km downstream in 10 hours.

$\bf \frac{25}{x - y} + \frac{35}{x + y} = 10...eq1$

and

In 15 hours, it can go 40 km upstream and 49km downstream

$\bf \frac{40}{x - y} + \frac{49}{x + y} = 15...eq2$

Step 2:

Simplify the equations.

Convert these equations in linear equations in two variables.

Let

$\bf \frac{1}{x + y} = b...eq3$

and

$\bf \frac{1}{x - y} = a...eq4$

Put the values form eq3 and eq4 in eq1 and eq2.

$\bf 25a + 35b = 10...eq5 \\ \bf 40a + 49b = 15...eq6$

Simplify the equations 5 and 6 to solve.

Cancel 5 from both sides and multiply eq 5 with 7 and subtract both equation 5 and 6.

$7(5a + 7b = 2)$

$35a + 49b = 14 \\ 40a + 49b = 15 \\ ( - ) \: \: \: \: ( - ) \: \: \: \: \: ( - )\\ - - - - - - - - \\ - 5a = - 1$

$\bf a = \frac{1}{5}...eq7$

Find the value of b.

Put value of a in eq6.

$40 \times \frac{1}{5} + 49b = 15$

$49b = 15 - 8$

$\bf b = \frac{1}{7} ...eq8$

Step 3:

Calculate the speed of the boat in still water and the speed of the stream.

$\frac{1}{x - y} = \frac{1}{5}$

so

$\bf x - y = 5...eq9$

and

$\frac{1}{ x + y} = \frac{1}{7}$

so

$\bf x + y = 7...eq10$

Solve both equations 9 and 10.

$x - y = 5 \\ x + y = 7 \\ - - - - - - \\ 2x = 12$

$\bf x = 6 \: kmph$

and

put the value of x in eq10.

$6 + y = 7$

$\bf y = 1 \: kmph$

Thus,

The speed of the stream is 1 kmph and the speed of the boat in still water is 6 kmph.

Learn more:

1) a motorboat whose speed in still water is 5 km per hour takes 1 hour more to go 12 km upstream then the return downstrea...

https://brainly.in/question/4558136

2) The speed of boat in still water is 15 km/h. It can go 30 km downstream and return back to its original point in 4 hrs 3...

https://brainly.in/question/4550104

#SPJ3