Question

A Rectangle with sides 100m and 50m. Person B and Person A start walking in the opposite direction at the same point with velocities 5m/s and 4m/s respectively. Person A starts walking 3 seconds after person B. How long would it take for them to meet on the other side of Rectangle

Answer 1

Answer:

It takes takes them 31.67 secs to meet after Person A starts walking

OR

34.67 secs after Person B starts walking

Step-by-step explanation:

First, we will find the perimeter of the rectangle

From,

Perimeter of rectangle = 2 ($l$ + $b$)

Where $l$ is the length

and $b$ is the breadth

From the question, $l$ = 100m

and $b$ = 50m

Hence,

Perimeter of the rectangle = 2 (100+50)

= 2(150) = 300m

Hence, the perimeter of the rectangle is 300m

This is the total distance that will be covered by both persons by the time they meet.

Let the distance covered by person A be $S_{1}$

and the distance covered by person B be $S_{2}$

We can write that

$S_{1}$ + $S_{2}$ = 300m

Velocity of person A, $V_{A}$ = 4 m/s

and velocity of person B, $V_{B}$ = 5 m/s

From the question, Person A starts walking 3 seconds after person B,

This means, if person A spends $t$ secs before they meet, then person B would spend (3 + $t$) secs.

For Person A,

Velocity = 4 m/s

Time = $t$ secs

Distance = $S_{1}$

From,

$Velocity = \frac{Distance}{Time}$

Then,

$Distance = Velocity \times time$

$S_{1} = 4 \times t$

$S_{1} = 4t$ ...... (1)

For Person B

Velocity = 5 m/s

Time = (t + 3) secs

Distance = $S_{2}$

Also, from

$Distance = Velocity \times time$

$S_{2} = 5 \times (3+t)$

$S_{2} = 5(3+t)$ ...... (2)

Recall that, $S_{1}$ + $S_{2}$ = 300m

Then, $S_{2}$ = 300m - $S_{1}$

We can then write that,

300m - $S_{1}$ $= 5(3+t)$

Then,

$S_{1} = 300 - 5(3+t)$ ..... (3)

Equating equations (1) and (3), we get

$300 - 5(3+t) = 4t$

$300 - 15 -5t = 4t\\9t = 285\\t = \frac{285}{9}$

$t = 31.67 secs$

This is the time spent by Person A

Hence, it takes takes them 31.67 secs to meet after Person A starts walking OR

34.67 secs after Person B starts walking