Question

Jane ran around the perimeter of a rectangular park at a constant rate of $10$ feet per second. The park has an area of $67,500$ square feet, and its length is exactly three times its width. For how many seconds did Jane run?

• A. $60$
• B. $120$
• C. $240$
• D. $360$
• E. $480$

Answer 1

The correct option is B $120$

Given, speed of running of Jane $=10$ feet per second
Area of the rectangular park $=67500$ sq feet
Let the width be $x$
Length will be $3x$ (as $3$ times of width)
As per question area will be area of rectangle is $=$ length $\times$ width
$\Rightarrow (3x\times x)=67500$
$\Rightarrow {3x}^2=67500$
$\Rightarrow x^2=\frac{67500}{3}=22500$
$\Rightarrow x=\sqrt{22500}=150$
Hence, width is $150$ feet
and length is $150\times 3=450$ feet
We know perimeter of a rectangle is $=2l+2w$
Perimeter will be $=$ $2\left(450\right)+2\left(150\right)$
$900+300=1200$feet
We know, time $=\frac{distance}{speed}$
$\therefore$ time taken by Jane will be $=$ $\frac{1200}{10}=120$ seconds.