Two people are 16 km apart on a straight road. They start walking

Leave a Comment / pair of linear equations / By preeti

Q) Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.

Ans:

STEP BY STEP SOLUTION

Let their speeds $x$ and $y$ kmph.

Let’s start with 1st case of “Walking in opposite direction”

Since in Opposite direction, effective speed will gets added

Hence, effective speed = $x + y$

Next, we know that time taken = $\frac{distance}{speed}$

Therefore, Time taken = $\frac{16}{x + y}$

It is given that during opposite direction walking, time taken is 2 hours

Therefore, $\frac{16}{x + y} = 2$

$\Rightarrow \frac{16}{2} = x + y$

$\Rightarrow x + y = 8$ ……………… (i)

Next, Let’s take 2nd case of “Walking in same direction”

Since in same direction, effective speed will be differential speed.

hence, effective speed = $x - y$

Next, we know that time taken = $\frac{distance}{speed}$

Therefore, Time taken = $\frac{16}{x - y}$

It is given that during same direction walking, time taken is 8 hours

Therefore, $\frac{16}{x - y} = 8$

$\Rightarrow \frac{16}{8} = x - y$

$\Rightarrow x - y = 2$ ……………… (ii)

By adding the equations (i) and (ii), we get:

$(x + y) + (x - y) = 8 + 2$

$\Rightarrow x + \cancel{y} + x - \cancel{y} = 10$

$\Rightarrow 2 x = 10$

$\Rightarrow x = 5$

By substituting value of $x$ in equation (i), we get:

$x + y = 8$

$\Rightarrow 5 + y = 8$

$\Rightarrow y = 8 - 5$

$\Rightarrow y = 3$

Therefore the walking speeds are 5 km/hr and 3 km/hr.

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