Question

A man can row 30 km upstream and 44 km downstream in 10 hours. also, he can row 40 km upstream and 55 km downstream in 13 hours. the rate of the current is

Answer 1

Let speed of still water is x km/h
speed of current is y km/h
Then, speed on upstream = (x - y) km/h
speed on downstream = (x + y) km/h

now, {time taken for 30 km upstream } + {time taken for 44 I'm downstream} = 10 hours
⇒ 30/(x - y) + 44/(x + y) = 10 --------(1)

similarly , {time taken for 40km upstream } + {time taken for 55 km downstream} = 13 hours
⇒ 40/( x - y) + 55/(x + y) = 13 --------(2)

4 × equation (1) - 3 × equation (2)
176/(x + y) - 165/(x + y) = 40 - 39 = 1
⇒ 11/(x + y) = 1 ⇒ x + y = 11 --------(3), put it in equation (1)
Then, (x - y) = 5 -----(4)

Solve equations (3) and (4),
2x = 11 + 5 ⇒x = 8 and y = 3

Hence, speed of still water is 8 km/h and speed of current is 3 km/h

Answer 2

Solution :-

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

so,

→ In upstream man speed = (x - y) km/h .

→ In downstream man speed = (x + y) km/h .

we know that,

• Time = Distance / speed .

so,

→ 40/(x - y) + 55/(x + y) = 13

→ 30/(x - y) + 44/(x + y) = 10

now, let us assume that,

• 1/(x - y) = u

1. 1/(x + y) = v

then,

→ 40u + 55 v = 13 -------- Eqn.(1)

→ 30u + 44 v = 10 -------- Eqn.(2)

Multiply Eqn.(1) by 3 and Eqn.(2) by 4 and subtracting result of Eqn.(1) from Eqn.(2) we get,

→ 4(30u + 44v) - 3(40u + 55v) = 4*10 - 3*13

→ 120u - 120u + 176v - 165v = 40 - 39

→ 11v = 1

→ v = (1/11)

putting value of v in Eqn.(1)

→ 40u + 55*(1/11) = 13

→ 40u + 5 = 13

→ 40u = 13 - 5

→ 40u = 8

→ u = (8/40)

→ u = (1/5)

therefore,

→ 1/(x - y) = u

→ 1/(x - y) = 1/5

→ x - y = 5

and,

→ 1/(x + y) = v

→ 1/(x + y) = 1/11

→ x + y = 11

adding both,

→ x - y + x + y = 5 + 11

→ 2x = 16

→ x = 8 km/h .

hence,

→ 8 + y = 11

→ y = 11 - 8

→ y = 3 km/h (Ans.)

Hence, Rate of current is 3 km/h.

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