Question

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,

it can go 40 km upstream and 55 km downstream. Determine the speed of the

stream and that of the boat in still water.​

Answer 1

Given :

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,it can go 40 km upstream and 55 km downstream.

Let the speed of boat in still water=x km\hr

The speed of stream=y km\hr

Speed of boat at downstream

⇒(x+y)km/hr

Speed of boat at upstream

⇒(x−y)km/hr

$time = \frac{distance \: }{speed \: }$

Time taken to cover 30 km upstream⇒

$= \frac{30}{x - y}$

Time taken to cover 44 km downstream⇒

$= \frac{44}{x + y}$

⇒ According to the first condition,

$= \frac{30}{x - y} = \frac{44}{x + y} = 10$

Time taken to cover 40 km upstream ⇒

$= \frac{44}{x - y}$

Time taken to cover 55 km downstream ⇒

$= \frac{55}{x + y}$

⇒According to the second condition,

$= \frac{44}{x - y} = \frac{55}{x + y} = 13$

let 1÷x-y = u and 1÷x+y= v

⇒30u+44v=10...(1)

⇒40u+55v=13...(2)

• Multiple 1 by 3 and 2 by 5 and subtract them both

⇒(150u+220v=50)−(160u+220v=52)

⇒−10u=−2⇒u= 1/5

PUT U = 1/5 IN EQ 1.

⇒ 30×1/5+44v = 10⇒44v=4 ⇒v = 1/4

⇒u= 1/x-y =1/5 ⇒x−y=5..(3)

⇒v= 1/x+y = 1/11⇒x+y=11..(4)

Subtracting 3 and 4, we get⇒x=8

put X = 8 in 4 EQ.

= x+y= 11 =y = 3

_________________

Hence, the speed of the boat in still water=8km\hr

The speed of stream=3km\hr

Hope it's helpful to you!

Answer 2

Answer:

Given :

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,it can go 40 km upstream and 55 km downstream.

Let the speed of boat in still water=x km\hr

The speed of stream=y km\hr

Speed of boat at downstream

⇒(x+y)km/hr

Speed of boat at upstream

⇒(x−y)km/hr

time = \frac{distance \: }{speed \: } time=

speed

distance

Time taken to cover 30 km upstream⇒

= \frac{30}{x - y} =

x−y

30

Time taken to cover 44 km downstream⇒

= \frac{44}{x + y} =

x+y

44

⇒ According to the first condition,

= \frac{30}{x - y} = \frac{44}{x + y} = 10=

x−y

30

=

x+y

44

=10

Time taken to cover 40 km upstream ⇒

= \frac{44}{x - y} =

x−y

44

Time taken to cover 55 km downstream ⇒

= \frac{55}{x + y} =

x+y

55

⇒According to the second condition,

= \frac{44}{x - y} = \frac{55}{x + y} = 13=

x−y

44

=

x+y

55

=13

let 1÷x-y = u and 1÷x+y= v

⇒30u+44v=10...(1)

⇒40u+55v=13...(2)

• Multiple 1 by 3 and 2 by 5 and subtract them both

⇒(150u+220v=50)−(160u+220v=52)

⇒−10u=−2⇒u= 1/5

PUT U = 1/5 IN EQ 1.

⇒ 30×1/5+44v = 10⇒44v=4 ⇒v = 1/4

⇒u= 1/x-y =1/5 ⇒x−y=5..(3)

⇒v= 1/x+y = 1/11⇒x+y=11..(4)

Subtracting 3 and 4, we get⇒x=8

put X = 8 in 4 EQ.

= x+y= 11 =y = 3

_________________

Hence, the speed of the boat in still water=8km\hr

The speed of stream=3km\hr

Step-by-step explanation:

#KeepLearning...