Question

Phoebe drives one-third of the distance from $A$ to $B$ at $x$ kilometers per hour, and she drives the other two-thirds of the distance at $y$ kilometers per hour. Calculate the Phoebe's average rate of speed, in kilometers per hour and in terms of $x$ and $y$ for the entire trip.

• A. $\frac{x+y}{2}$
• B. $\frac{x+2y}{3}$
• C. $\frac{2x+y}{3}$
• D. $\frac{xy}{x+y}$
• E. $\frac{3xy}{2x+y}$

Answer 1

The correct option is E $\frac{3xy}{2x+y}$

Let Phoebe drives distance $AB$ is $3d$

For first d kilometer the Phoebe drives at x km\hr time taken $=$ $\frac{d}{x}$

For the next $2d$ kilometer the Phoebe drives at $y$ km\hr

So time taken $=$ $\frac{2d}{y}$

Then average rate $=$ $\frac{3d}{\frac{d}{x}+\frac{2d}{y}}$

$=$ $\frac{3d}{\frac{dy}{xy}+\frac{2dx}{xy}}$

$=$ $\frac{3d}{\frac{dy+2dx}{xy}}$

$=$ $\frac{3dxy}{dy+2dx}$

$=\frac{3xy}{2x+y}$