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: 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 gets subtracted

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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