Question

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

Answer 1

Let speed of the boat in still water = x km/hr, and

Speed of the current = y km/hr

Downstream speed = (x+y) km/hr

Upstream speed = (x - y) km/hr

$t = \frac{d}{s}$

$\frac{24}{x + y} + \frac{16}{x - y} = 6...(1)$

$\frac{36}{x + y} + \frac{12}{x - y} = 6...(2)$

$putting \: \frac{1}{x + y} = u \: and \frac{1}{x - y} = v \: the \: equations \: become = >$

24u + 16v = 6

Or, 12u + 8v = 3... (3)

36u + 12v = 6

Or, 6u + 2v = 1... (4)

Multiplying (4) by 4, we get,

24u + 8v = 4… (5)

Subtracting (3) by (5), we get,

12u = 1

$= > u = \frac{1}{12}$

Putting the value of u in (4), we get, v =

$\frac{1}{4}$

$\frac{1}{x + y} = \frac{1}{12} \: and \: \frac{1}{x - y} = \frac{1}{4}$

$x + y = 12 \: and \: x - y = 4$

Thus, speed of the boat upstream = 4 km/hr

Speed of the boat downstream = 12 km/hr

hope it helps you✨

Answer 2

Answer:

Let speed of the boat in still water = x km/hr, and

Speed of the current = y km/hr

Downstream speed = (x+y) km/hr

Upstream speed = (x - y) km/hr

t = \frac{d}{s}t=

s

d

\frac{24}{x + y} + \frac{16}{x - y} = 6...(1)

x+y

24

+

x−y

16

=6...(1)

\frac{36}{x + y} + \frac{12}{x - y} = 6...(2)

x+y

36

+

x−y

12

=6...(2)

putting \: \frac{1}{x + y} = u \: and \frac{1}{x - y} = v \: the \: equations \: become = >putting

x+y

1

=uand

x−y

1

=vtheequationsbecome=>

24u + 16v = 6

Or, 12u + 8v = 3... (3)

36u + 12v = 6

Or, 6u + 2v = 1... (4)

Multiplying (4) by 4, we get,

24u + 8v = 4… (5)

Subtracting (3) by (5), we get,

12u = 1

= > u = \frac{1}{12}=>u=

12

1

Putting the value of u in (4), we get, v =

\frac{1}{4}

4

1

\frac{1}{x + y} = \frac{1}{12} \: and \: \frac{1}{x - y} = \frac{1}{4}

x+y

1

=

12

1

and

x−y

1

=

4

1

x + y = 12 \: and \: x - y = 4x+y=12andx−y=4

Thus, speed of the boat upstream = 4 km/hr

Speed of the boat downstream = 12 km/hr

Step-by-step explanation:

thanku