Ex 3.6, 2
Formulate the following problems as a pair of equations, and hence find their solutions:
(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water & speed of the current.
Let the speed of boat in still water be x km/hr
& let the speed of current be y km/hr
Now,
Speed downstream = x + y
Speed upstream = x – y
Ritu can row 20 km
downstream in 2 hours
For downstream
Distance = 20 km
Time = 2 hours
Speed = x + y
We know that
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
x + y = 20/2
x + y = 10
Ritu can row 4 km
upstream in 2 hours
For upstream
Distance = 4 km
Time = 2 hours
Speed = x – y
We know that
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
x – y = 4/2
x – y = 2
Hence, our equations are
x + y = 10 …(1)
x – y = 2 …(2)
From (1)
x + y = 10
x = 10 – y
Putting x = 10 – y in (2)
x – y = 2
(10 – y) – y = 2
– 2y = 2 – 10
– 2y = −8
y = (−8)/(−2)
y = 4
Putting y = 4 in (1)
x + y = 10
x + 4 = 10
x = 10 – 4
x = 6
Thus, x = 6, y = 4 is the solution
Hence
Speed of boat in still water = x = 6 km/hr
Speed of stream = y = 4 km/hr

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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