Question

A boat goes 30+km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream and 55 km downstream. Determine the speed of the​

Answer 1

Answer:

above

Step-by-step explanation:

hoping it was helpful

Answer 2

Let us assume that

Speed of stream = ykm/h

speed of boat in still water = xkm/h

So, speed in upstream = x-ykm/h

& speed in downstream = x+ykm/h

According to the first situation,

Time = Distance/speed

$\frac{30}{x - y} + \frac{44}{x + y} = 10 \: \: \: \: \: \: ........(1)$

According to the second situation,

$\frac{40}{x - y} + \frac{55}{x + y} = 13 \: \: \: \: \: \: .......(2)$

Let us take,

1/x-y = p ......(3)

1/x+y = q ........(4)

30p + 44p = 10

p = 10-44q/30

40p + 55q = 30 ......(5)

Putting the value of x in eqn (5)

$\frac{40 \times (10 - 44q)}{30} + \frac{55}{1}q = 13$

$\frac{400 - 1560q}{30} + \frac{55}{1} q = 13$

$\frac{400 - 1560q + 1650}{30} = 13$

400-110q = 13

-110q = -10

q = 1/10

$p = \frac{10 - 44 \times \frac{1}{11} }{30}$

$\: \: \: \: = \frac{10 - 4}{30}$

$\: \: \: \: = \frac{6}{30}$

$\: \: \: p= \frac{1}{5}$

Now by eqn (3) & (4)

$\frac{1}{x - y} = p \:$

$\frac{1}{x - y} = \frac{1}{5} \\ x - y = 5 \\ x = 5 + y \: \: \: \: ....(5)$

$\frac{1}{x + y} = q \\ \frac{1}{x + y} = \frac{1}{11} \\ x + y = 11$

putting the value of x in eqn (5)

5+y+y=11

2y=6

y=3

x=5+y

x= 5+3

x=8

So, speed of the stream = 3km/hr.

stream of the boat in still water = 8km/hr.

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