Question

2. Formulate the following problems as a pair of equations, and 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.​

Answer 1

her speed in still water = 11 km/hour

the speed of the current = 9 km/hour

Explanation:

x = Ritu's speed of rowing.

y = the sites of the river water flowing

x + y = 20 km / 2 hours = 10 km / hour

x - y = 4 km / 2 hours = 2 km / hour

x = 2 + y

2 + y + y = 20

2y = 18

y = 9 km/hour

x = 2 + y = 2 + 9 = 11 km/hour

Answer 2

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Let speed of Ritu

in still water be x km/hr.

in current water be y km/hr.

Speed of water while upstream is (x + y) km/hr,

downstream is (x – y) km/hr,

2(x + y) = 20 x + y = 10 ………… (i)

2(x – y) = 4 x – y = 2 …………… (ii)

By Adding eqn. (i) and eqn.

x + y = 10

x - y = 2

_______________

x = 12

`x = (12)/(2) = 6`

(ii), Substituting the value,

x = 6 in eqn.

(i), x + y = 10 6 + y = 10 y = 10 – 6

∴ y = 4

∴ Speed of Ritu in still water, x = 6 km/hr. in current water, y = 4 km/hr.