Question

Formulate the following problems as a pair of equations,hence find their solutions.

1. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.(Based on NCERT Text book)

Answer 1

Speed downstream = 10 Kmph
Speed upstream = 2 Kmph

Let x = speed of rowing 
      y = speed of the current
x + y = 10
x - y = 2
x = 6 y = 4 

Speed of rowing = 6 Kmph
Speed of the current = 4 Kmph

Answer 2

Her speed of rowing in still water = 6 km. per hour ...
the speed of the current = 4 km. per hour ..


let her speed in still water = X km. / hour ..
let the speed of the current = Y km. / hour ...

so her speed of rowing in downstream = (X + Y) km. / hour ..

since .. speed = distance / time

so .. X + Y = 20 / 2

X + Y = 10 ............... (1)



now ... her speed of rowing in upstream = (X - Y) km. / hour ...

again by the rule .... S = D / t

so ..... (X -Y) = 4 / 2

(X - Y) = 2 ......... (2)




by adding equation (1) and (2) ...

X + Y + X - Y = 10 + 2

2X = 12
so ..

X = 12 / 2

X = 6 km. / hour ...

by equation (1) ..

X + Y = 10

6 + Y = 10

Y = 10 - 6 = 4

Y = 4 km. / hour ....