Question

A man can row 50 km upstream and 72 km downstream in 9 hours. he can also row 70 km upstream and 90 km downstream in 12 hours. find the rate of current.

Answer 1

Let the speed upstream be x and the speed downstream be y.

If he rows 50km upstream and 72km downstream the time is :

50/x + 72/y = 9....... 1

If he rows 70km upstream and 90km downstream the time taken is :

70/x + 90/y = 12....... 2

We can obtain y from 2:

70y + 90x = 12xy

70y - 12xy = - 90x

35y - 6xy = - 45x

Y(35 - 6x) = - 45x

Y = - 45x / (35 - 6x)

Substituting this in 1:

50/x + 72 (35 - 6x)/-45x = 9

50 - 8/5(35 - 6x) = 9x

50 × 5 - 280+ 48x = 45x

250 - 280 = 45x - 48x

-30 = - 3x

X = 30/3= 10 km/h

Substituting this in 2:

70/10 + 90/y = 12

7y + 90 = 12y

12y - 7y = 90

5y = 90

Y = 90/5

Y = 18 km/h

Now let the speed of the boat be x.

Speed upstream = speed of the boat - speed of the current

Speed of current = 10 + x

Speed downstream = speed of the boat + speed of current

Speed of current = 18 - x

Equating the two :

18 - x = 10 + x

8 = 2x

x = 8/2

x = 4km/h

Speed of current equals:

10 + 4 = 14km/h