Ritu can row downstream $20 ext{ km}$ in $2 ext{ hours}$, and upstream $4 ext{ km}$ in $2 ext{ hours}$. Formulate th

Question

Ritu can row downstream $20	ext{ km}$ in $2	ext{ hours}$, and upstream $4	ext{ km}$ in $2	ext{ hours}$. Formulate the system of linear equations representing this situation. Find her speed of rowing in still water and the speed of the current using the elimination method. Show complete step-by-step calculations and verification.

Accepted Answer

Step 1: Define variables
Let the speed of Ritu in still water = $x	ext{ km/h}$
Let the speed of the stream (current) = $y	ext{ km/h}$ Step 2: Determine relative speeds Speed downstream $= (x + y)	ext{ km/h}$ Speed upstream $= (x - y)	ext{ km/h}$ 
We know the formula: $$	ext{Speed} = \frac{	ext{Distance}}{	ext{Time}} \quad \implies \quad 	ext{Distance} = 	ext{Speed} 	imes 	ext{Time}$$ Step 3: Formulate Linear Equations Condition 1: Downstream motion Distance = $20	ext{ km}$, Time = $2	ext{ hours}$ $$(x + y) 	imes 2 = 20$$ $$x + y = 10 \quad 	ext{--- (Equation 1)}$$ Condition 2: Upstream motion Distance = $4	ext{ km}$, Time = $2	ext{ hours}$ $$(x - y) 	imes 2 = 4$$ $$x - y = 2 \quad 	ext{--- (Equation 2)}$$ --- Step 4: Solve the system using Elimination Method 
Adding Equation (1) and Equation (2): $$(x + y) + (x - y) = 10 + 2$$ $$2x = 12$$ $$x = \frac{12}{2} = 6$$ 
Substitute $x = 6$ into Equation (1): $$6 + y = 10$$ $$y = 10 - 6 = 4$$ --- Step 5: Verification of Results Downstream speed $= 6 + 4 = 10	ext{ km/h}$ Time taken $= \frac{20}{10} = 2	ext{ hours}$ (Matches given data) Upstream speed $= 6 - 4 = 2	ext{ km/h}$ Time taken $= \frac{4}{2} = 2	ext{ hours}$ (Matches given data) Final Answer Speed of rowing in still water $= 6	ext{ km/h}$ Speed of the current $= 4	ext{ km/h}$

Pair of Linear Equations in Two Variables

❓ Sibling Questions in this Chapter