Question

A boat takes 6hours to travel 8km upstream and 32km downstream and it takes 7 hours to tarvel 20km upstream and 16km downstream.find the speed of the boat in still
water And the speed of the stream

Answer 1

Answer:

upstream 20 km do

Step-by-step explanation:

8 hours of

upstream

Answer 2

Solution :-

Let us assume that, speed of boat in still water is x km/h and speed of stream is y km/h .

so,

→ 8/(x - y) + 32/(x + y) = 6

→ 20/(x - y) + 16/(x + y) = 7

let ,

• 1/(x - y) = m
• 1/(x + y) = n

then,

→ 8m + 32n = 6

→ 8(m + 4n) = 6

→ m + 4n = (3/4) ------ Eqn.(1)

and,

→ 20m + 16n = 7

→ 4(5m + 4n) = 7

→ 5m + 4n = (7/4) ------- Eqn.(2)

subtracting Eqn.(1) from Eqn.(2),

→ (5m + 4n) - (m + 4n) = (7/4) - (3/4)

→ 4m = 4/4

→ m = (1/4)

putting value of m in Eqn.(1) ,

→ (1/4) + 4n = 3/4

→ 4n = 3/4 - 1/4

→ 4n = 2/4

→ n = 1/8

therefore,

→ 1/(x - y) = m

→ x - y = 4 ------ Eqn.(3)

and,

→ 1/(x + y) = n

→ x + y = 8 -------- Eqn.(4)

adding Eqn.(3) & (4) now,

→ x - y + x + y = 12

→ 2x = 12

→ x = 6 km / h

putting value of x in Eqn.(3),

→ 6 - y = 4

→ y = 6 - 4

→ y = 2 km / h

Hence, the speed of the boat in still water is 6 km/h and the speed of the stream is 2 km/h .

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