Question

Example 19: 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
down-stream. Determine the speed
of the stream and that of the boat in
still water​

Answer 1

Heyy army!!!

Answer:

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

Time taken to cover 30 km upstream ⇒ 30/x-y

Time taken to cover 44 km downstream⇒ 44/x+y

According to the first condition,

⇒ 30/x−y =44/ x+y =10

Time taken to cover 40 km upstream ⇒ 40/x-y

Time taken to cover 55 km downstream ⇒ 55/x+y

According to the second condition,

⇒ 40/x-y = 55/ x+y =13

Let 1/x−y=u and 1/x+y=v

⇒30u+44v=10.....eq1

⇒40u+55v=13.....eq2

Multiplying eq1 by 3 and eq2 by 5 and subtract both

⇒(150u+220v=50)−(160u+220v=52)

⇒−10u=−2⇒u= 1/5

put u= 1/5

in eq1

⇒30× 1/5+44v=10⇒44v=4⇒v= 1/4

⇒u= 1/x−y= 1/5

⇒x−y=5...eq3

⇒v= 1/x+y = 1/11

⇒x+y=11...eq4

Subtracting eq3 and eq4, we get

⇒x=8

Put x=8 in eq3

⇒y=3

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

The speed of stream=3km\hr

I hope it might help you

Take care and stay safe

Purple you❤❤