Multiple choice

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.

  1. $\dfrac {x+y}{2}$
  2. $\dfrac {x+2y}{3}$
  3. $\dfrac {2x+y}{3}$
  4. $\dfrac {xy}{x+y}$
  5. $\dfrac {3xy}{2x+y}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Average speed = Total distance / Total time. Let distance be 3D. Time = (D/x) + (2D/y) = (Dy + 2Dx) / xy. Average speed = 3D / ((Dy + 2Dx) / xy) = 3xy / (2x + y).

AI explanation

Let the total distance be 3D, meaning the first part is distance D at speed x and the second part is distance 2D at speed y. The total time taken is the sum of the times for each part, calculated as D divided by x plus 2D divided by y. Average speed equals total distance divided by total time, giving 3D divided by the sum of (D divided by x) and (2D divided by y). Simplifying this expression by factoring out D yields 3 divided by the sum of (1 divided by x) and (2 divided by y), which simplifies to 3xy divided by the sum of y and 2x.

Keep practicing — related questions