Question

A person can grow 4km upstream and 16km downstream in 1 hour 50 minutes. He can row 20km downstream and 20km upstream in 4 hours 10 minutes. Find the speed of the person in still water and the speed of the current

Answer 1

Answer:

Speed of the person in still water be 12 km/hr

Speed of the current be 2 km/hr

Step-by-step explanation:

Let the speed of the person in still water be x km/hr

Let the speed of the current be y km/hr

In upstream, the speed = (x - y) km/hr

In downstream, the speed = (x + y) km/hr

Also, distance, speed and time are related as

Distance = Speed × Time

Given that a person can row 4 km upstream and 16 km downstream in 1 hour 50 minutes

We have

4/(x - y) + 16/(x + y) = 11/6 ---- (1)

Also, the person can row 20 km downstream and 20 km upstream in 4 hours 10 minutes, we have

20/(x - y) + 20/(x + y) = 25/6 ---- (2)

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

Thus, we have

4u + 16v = 11/6

24u + 96v = 11 ----- (3)

Also, 20u + 20v = 25/6

        4u + 4v = 5/6

        24u +24v = 5 ---- (4)

Solving (3) and (4), we get

 24u + 96v = 11

 24u + 24v = 5

(-)       (-)        (-)

-----------------------------

0u + 72v = 6

    v = 6/72

    v = 1/12

Also, putting the value of v in (4)

24u + 24 × 1/12 = 5

24u + 2 = 5

24u = 3

u = 3/24

u = 1/8

Thus, value of x and y are calculated as follows:

1/(x - y) = 1/8

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

and

1/(x + y) = 1/12

x + y = 12 ----- (6)

Again solving (5) and (6), we get

 x - y = 8

 x + y = 12

------------------

2x = 20

x = 10

Putting the value of x in  (6), we get

10 + y =12

y = 2

Thus,

Speed of the person in still water be 12 km/hr

Speed of the current be 2 km/hr