Question

A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours. In the same time, it covers a distance of 12 km upstream and 36 km downstream. Find the speed of the boat in still water and that of the stream.


helppp
don't u dare spam ...
or I'll r .e.p..or..t. at least 30ans of urs​

Answer 1

Let the speed of the boat be x and Speed of the stream be y.

• speed For Upstream = (x – y)
• speed for Downstream = (x + y)

As We know that motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hrs.

→ 16/(x –y) + 24/(x + y) = 6 •••[1]

As we also know that In the same time, it covers a distance of 12 km upstream and 36 km downstream.

→ 12/(x –y) + 36/(x+y) = 6 •••[2]

^Let the 1/(x–y) be a and 1/(x+y) be b.

16a + 24b = 6 •••[3]

12a + 36b = 6 •••[4]

★After Calculating Equation [3] and [4],

we got that b = 1/12

For getting the value of "a" we'll put value of "b in [3] or [4].

→ 12a + 36b = 6

→ 12a + 36×1/12 = 6

→ 12a + 3 = 6

→ 12a = 3

→ a = ¼

• a = 1/(x–y) = ¼

→ (x – y) = 4

• b = 1/(x + y) = 1/12

→ (x + y) = 12

Finally, We got that:

» (x – y) = 4

» (x + y) = 12

→ 2x = 16

→ x = 8 km/hr

→ x + y = 12

→ 8 + y = 12

→ y = 4 km/hr

Hence,

The Speed of the boat and stream is 8 km/hr and 4 km/hr Respectively.

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

Speed of the boat in still water be 'x' km per hour

Speed of stream be 'y' km per hour.

So,

Speed of upstream = x - y km per hour

Speed of downstream = x + y km per hour

Case :- 1

A motorboat covers a distance of 16 km upstream and 24 km downstream in 6 hours.

Time taken to cover 16 km upstream with the speed of x - y km per hour is

$\sf \: \dfrac{16}{x - y}$

And

Time taken to cover 24 km downstream with the speed of x + y km per hour is

$\sf \: \dfrac{24}{x + y}$

According to statement, Total time taken is 6 hours.

$\rm :\longmapsto\:\dfrac{16}{x - y} + \dfrac{24}{x + y} = 6$

can be rewritten as

$\rm :\longmapsto\:\dfrac{8}{x - y} + \dfrac{12}{x + y} = 3 - - - (1)$

Case : - 2

it covers a distance of 12 km upstream and 36 km downstream in 6 hours

Time taken to cover 12 km upstream with the speed of x - y km per hour is

$\sf \: \dfrac{16}{x - y}$

And

Time taken to cover 36 km downstream with the speed of x + y km per hour is

$\sf \: \dfrac{36}{x + y}$

According to statement, Total time taken is 6 hours.

$\rm :\longmapsto\:\dfrac{12}{x - y} + \dfrac{36}{x + y} = 6$

can be rewritten as

$\rm :\longmapsto\:\dfrac{2}{x - y} + \dfrac{6}{x + y} = 1 - - - - (2)$

Now we have two equations,

$\rm :\longmapsto\:\dfrac{8}{x - y} + \dfrac{12}{x + y} = 3 - - - (1)$

and

$\rm :\longmapsto\:\dfrac{2}{x - y} + \dfrac{6}{x + y} = 1 - - - - (2)$

Let assume that

$\rm :\longmapsto\:\dfrac{1}{x - y} = a \: \: \: and \: \: \: \dfrac{1}{x + y} = b$

So, equation (1) and (2) can be rewritten as

$\rm :\longmapsto\:8a + 12b = 3 - - - (3)$

and

$\rm :\longmapsto\:2a + 6b = 1$

can be rewritten as on multiply by 2,

$\rm :\longmapsto\:4a + 12b = 2 - - - (4)$

On Subtracting equation (4) from (3), we get

$\rm :\longmapsto\:4a = 1$

$\rm :\implies\:a = \dfrac{1}{4}$

Now, Substitute the value of a in equation (4), we get

$\rm :\longmapsto\:1 + 12b = 2$

$\rm :\longmapsto\:12b = 2 - 1$

$\rm :\longmapsto\:12b = 1$

$\rm :\implies\:b = \dfrac{1}{12}$

So,

Now,

$\rm :\longmapsto\:a = \dfrac{1}{4}$

$\rm :\longmapsto\:\dfrac{1}{x - y} = \dfrac{1}{4}$

$\rm :\implies\:x - y = 4 - - - (5)$

and

$\rm :\longmapsto\:b = \dfrac{1}{12}$

$\rm :\longmapsto\:\dfrac{1}{x + y} = \dfrac{1}{12}$

$\rm :\implies\:x + y = 12 - - - (6)$

Now, on adding equation (5) and equation (6), we get

$\rm :\longmapsto\:2x = 16$

$\bf\implies \:x = 8$

On substituting the value of x in equation (6), we get

$\rm :\longmapsto\:8 + y = 12$

$\rm :\longmapsto\: y = 12 - 8$

$\bf\implies \:y = 4$

Hence,

Speed of boat in still water = 8 km per hour

Speed of stream = 4 km per hour