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

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=1/11

⇒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