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

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

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

$x = \frac{12}{2} = 6$

(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.

Answer 2

Answer:

her speed in still water = 11 km/hour

the speed of the current = 9 km/hour

Step-by-step 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