Question

4
drag each tile to the correct box.
lori’s family is on a road trip. they split their drive into the five legs listed in the table. find the average velocity for each leg of the trip. then arrange the legs of the trip from lowest velocity to highest.

leg	distance (km)	time (min)
b	20	15
c	24	12
d	36	9
e	14	14

leg a leg b leg c leg d leg e
□ → □ → □ → □ → □

Explanation:

Step1: Recall average velocity formula

Average velocity \( v = \frac{\text{Distance (km)}}{\text{Time (h)}} \), convert time from minutes to hours by dividing by 60.

Step2: Calculate velocity for Leg A

Distance = 15 km, Time = 10 min = \( \frac{10}{60} = \frac{1}{6} \) h.
\( v_A = \frac{15}{\frac{1}{6}} = 15 \times 6 = 90 \) km/h.

Step3: Calculate velocity for Leg B

Distance = 20 km, Time = 15 min = \( \frac{15}{60} = \frac{1}{4} \) h.
\( v_B = \frac{20}{\frac{1}{4}} = 20 \times 4 = 80 \) km/h.

Step4: Calculate velocity for Leg C

Distance = 24 km, Time = 12 min = \( \frac{12}{60} = \frac{1}{5} \) h.
\( v_C = \frac{24}{\frac{1}{5}} = 24 \times 5 = 120 \) km/h. Wait, no, wait: 12 minutes is 0.2 hours. \( 24 / 0.2 = 120 \)? Wait, no, 12 minutes is \( 12/60 = 0.2 \) hours. 24 / 0.2 = 120? Wait, no, 24 divided by 0.2 is 120? Wait, no, 24 / 0.2 = 120? Wait, no, 24 divided by (12/60) = 24 (60/12) = 24 5 = 120. Correct.

Wait, no, wait Leg D: Distance 36 km, Time 9 min = 9/60 = 0.15 h. \( 36 / 0.15 = 240 \)? Wait, no, 9 minutes is 0.15 hours? 9/60 = 3/20 = 0.15. 36 / 0.15 = 240? Wait, that can't be right. Wait, no, maybe I made a mistake. Wait, average velocity is distance over time, time in hours. Let's recalculate:

Leg A: 15 km, 10 min = 10/60 = 1/6 h. 15 / (1/6) = 90 km/h. Correct.

Leg B: 20 km, 15 min = 15/60 = 1/4 h. 20 / (1/4) = 80 km/h. Correct.

Leg C: 24 km, 12 min = 12/60 = 1/5 h. 24 / (1/5) = 120 km/h. Correct.

Leg D: 36 km, 9 min = 9/60 = 3/20 h. 36 / (3/20) = 36 * (20/3) = 240 km/h. Wait, that's very high, but maybe.

Leg E: 14 km, 14 min = 14/60 = 7/30 h. 14 / (7/30) = 14 * (30/7) = 60 km/h. Ah, there we go. I miscalculated Leg E earlier. So Leg E: 14 km in 14 minutes. 14 minutes is 14/60 hours. So 14 divided by (14/60) = 60 km/h. That makes more sense.

So let's redo:

Leg A: 15 km / 10 min = 15 / (10/60) = 15 * 6 = 90 km/h.

Leg B: 20 km / 15 min = 20 / (15/60) = 20 * 4 = 80 km/h.

Leg C: 24 km / 12 min = 24 / (12/60) = 24 * 5 = 120 km/h.

Leg D: 36 km / 9 min = 36 / (9/60) = 36 (60/9) = 36 (20/3) = 240 km/h. Wait, 94=36, so 60/9=20/3. 36(20/3)=240. Correct.

Leg E: 14 km / 14 min = 14 / (14/60) = 60 km/h.

Now, list the velocities:

Leg E: 60 km/h

Leg B: 80 km/h

Leg A: 90 km/h

Leg C: 120 km/h

Leg D: 240 km/h

So from lowest to highest: Leg E, Leg B, Leg A, Leg C, Leg D.

Wait, let's confirm:

Leg E: 60

Leg B: 80 (60 < 80)

Leg A: 90 (80 < 90)

Leg C: 120 (90 < 120)

Leg D: 240 (120 < 240)

Yes. So the order is E, B, A, C, D.

Answer:

leg E → leg B → leg A → leg C → leg D