Question

At $10:00$, Angela starts from her home and runs at a constant pace to Kathleens house, which is exactly $2$ miles away. Immediately, she and Kathleen turn around and walk back to Angelas house exactly $4$ miles an hour slower than Angela ran. When they arrive at Angelas house, the time is $10:45$. At what speed did Angela run?

• A. $6$ miles per hour
• B. $6.5$ miles per hour
• C. $7$ miles per hour
• D. $7.5$ miles per hour
• E. $8$ miles per hour

Answer 1

The correct option is E $8$ miles per hour

Let speed of angle be '$x$' miles/hr.
Distance between Angela and Kathleens house $=2$ miles
Time taken by Angela to reach Kathleens house $=\frac{2}{x}$
A.T.Q.
$\frac{2}{x}+\frac{2}{x-4}=\frac{45}{60}$
$\Rightarrow \frac{2(x-4)+2x}{x(x-4)}=\frac{3}{4}$
$\Rightarrow (4x-8)4=3(x^2-4x)$
$\Rightarrow 16x-32=3x^2-12x$
$\Rightarrow 3x^2-28x+32=0$
$\Rightarrow 3x^2-24x-4x+32=0$
$\Rightarrow 3x(x-8)-4(x-8)=0$
$\Rightarrow (x-8)(3x-4)=0$
$\Rightarrow x=8$, $x=\frac{4}{3}$
Here $x=\frac{4}{3}$ is rejected [$\because x-4$ will be less than 0 if ere $x=\frac{4}{3}$.
$\Rightarrow x=8$
Therefore, speed of Angela is $8$ miles/hr.