Question

Two men P and Q are standing at corners A and B of square ABCD of side 8 m. They start moving along the track with constant speed $2{m}/{s}\;$and $10{m}/{s}\;$ respectively. The time when they will meet for the first time, is equals to
A. 2 sec
B. 3 sec
C. 1 sec
D. 6 sec

Answer 1

The relation between the speed of a body, the total distance travelled by the body and the time taken by that body should be used to solve this problem. The relation is, the speed of a body equals the distance covered by that body by the time taken to cover the distance by that body.
Formula used:
$S=\dfrac{d}{t}$

Complete answer:
From the given information, we have the data as follows.
Two men P and Q are standing at corners A and B of square ABCD of side 8 m. They start moving along the track with constant speed $2{m}/{s}\;$and $10{m}/{s}\;$respectively.
The mathematical representation of the same is,
The distance between two men P and Q is 8 m.
From the other way, the distance between two men P and Q is, $d=8m$
The constant speed of man P standing along the corner A is, $2{m}/{s}\;$
The constant speed of man Q standing along the corner B is, $10{m}/{s}\;$
From the other way, the person Q has to cover a distance of, $3\times 8=24m$
The constant speed of men is, $10-2=8{m}/{s}\;$
The relation is, the speed of a body equals the distance covered by that body by the time taken to cover the distance by that body.
$S=\dfrac{d}{t}$
Substitute the values in the above formula.

& 8=\dfrac{24}{t} \\\ & \Rightarrow t=\dfrac{24}{8} \\\ & \therefore t=3s \\\ \end{aligned}$$ $$\therefore $$ The time when two men P and Q meet for the first time, is equal to 3 sec. **Thus, option (B) is correct.** **Note:** The relation is, the speed of a body equals the distance covered by that body by the time taken to cover the distance by that body. The distance between the remaining sides of the square should be used to solve this problem.