Class 10MathematicsPair of Linear Equations in Two VariablesMix Examples - Pair of Linear Equations in Two Variables
EasyFormulate the following problems as a pair of equations, and hence find their solutions:
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.
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.
(A) Let the speed of Ritu in still water be $x\, km/h$ and the speed of the stream be $y\, km/h$.
Speed of Ritu while rowing:
Upstream $= (x - y)\, km/h$
Downstream $= (x + y)\, km/h$
According to the problem:
For downstream: $2(x + y) = 20 \Rightarrow x + y = 10$ $...(1)$
For upstream: $2(x - y) = 4 \Rightarrow x - y = 2$ $...(2)$
Adding equations $(1)$ and $(2)$:
$(x + y) + (x - y) = 10 + 2$
$2x = 12 \Rightarrow x = 6$
Substituting $x = 6$ in equation $(1)$:
$6 + y = 10 \Rightarrow y = 4$
Hence, Ritu's speed in still water is $6\, km/h$ and the speed of the current is $4\, km/h$.
Speed of Ritu while rowing:
Upstream $= (x - y)\, km/h$
Downstream $= (x + y)\, km/h$
According to the problem:
For downstream: $2(x + y) = 20 \Rightarrow x + y = 10$ $...(1)$
For upstream: $2(x - y) = 4 \Rightarrow x - y = 2$ $...(2)$
Adding equations $(1)$ and $(2)$:
$(x + y) + (x - y) = 10 + 2$
$2x = 12 \Rightarrow x = 6$
Substituting $x = 6$ in equation $(1)$:
$6 + y = 10 \Rightarrow y = 4$
Hence, Ritu's speed in still water is $6\, km/h$ and the speed of the current is $4\, km/h$.
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