Question

multiple choice question
albert and bob decide to have a swimming race in which they will swim from one end of the pool to the other and back again. bob completes the race first, ending up back at the start. albert gets to the other end of the pool the fastest. choose the true statement below.
○ bob has the greater average speed but albert has the greater average velocity.
○ bob has the greater average speed and average velocity.
○ albert has the greater average speed but bob has the greater average velocity.
○ albert has the greater average speed and average velocity.

Explanation:

Step1: Define average speed

Average speed = $\frac{\text{Total distance}}{\text{Total time}}$

Step2: Define average velocity

Average velocity = $\frac{\text{Total displacement}}{\text{Total time}}$

Step3: Analyze Bob's metrics

Bob's total distance = $2L$ (pool length $L$, round trip). Total time $t_B < t_A$ (he finishes first). His total displacement = $0$ (starts/ends at start).
Average speed: $v_{s,B} = \frac{2L}{t_B}$; Average velocity: $v_{v,B} = \frac{0}{t_B} = 0$

Step4: Analyze Albert's metrics

Albert's total distance = $L$ (only to the other end). Total time $t_A > t_B$. His total displacement = $L$ (starts at one end, ends at the other).
Average speed: $v_{s,A} = \frac{L}{t_A}$; Average velocity: $v_{v,A} = \frac{L}{t_A}$

Step5: Compare speeds/velocities

Since $t_B < t_A$, $\frac{2L}{t_B} > \frac{L}{t_A}$, so Bob's average speed is greater. Albert's average velocity ($\frac{L}{t_A}$) is greater than Bob's ($0$).

Answer:

Bob has the greater average speed but Albert has the greater average velocity.