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

Answer:

See process below

Step-by-step explanation:

Take 10=30/(vb-vw)

And 13=(40/(vb-vw))+(55/(vb+vw))

Then solve for vw

And vb is velocity of boat

Done.

Answer 2

Step-by-step explanation:

Let's say the speed of the stream is x km/hr and of the boat in still water is y km/hr.

Upstream speed = (y - x) km/hr

Downstream speed = (y + x) km/hr

Time = Distance/Speed

The boat goes 30 km upstream and 44 km downstream in 10 hours.

Time taken = 30/(y - x) + 44/(y + x)

10 = 30/(y - x) + 44/(y + x) ---------- (1)

The boat goes 40 km upstream and 55 km downstream in 13 hours.

Time taken = 40/(y - x) + 55/(y + x)

13 = 40/(y - x) + 55/(y + x) --------- (2)

Let's say 1/(y - x) = u and 1/(y + x) = v

Therefore,

From (1) and (2)

30u+44v=10 ---------- (3)

40u+55v=13 ----------- (4)

Multiply eq (3) with 4 and eq (4) with 3

120u + 176v = 40 -------- (5)

120u + 165 v = 39 -------- (6)

Subtract eq (6) from (5). On solving we get,

v = 11

So,

1/(y + x) = v

y + x = 11 -------- (7)

Similarly,

u = 1/5

And 1/(y - x) = u

y - x = 5 ---------- (8)

On adding eq (7) & (8) we get,

2y = 16

y = 8

Substitute value of y in (7)

8 + x = 11

x = 3

Therefore, the speed of the stream is 3 km/hr and of the boat in still water is 8 km/hr.