Question

if a car travels 200 kilometers in 110 minutes, how fast (in m/s) is it traveling? 1 point 0.03 m/s jeff and amy want to ride their bikes from their neighborhood to school which is 14.4 km away. it takes amy 35 minutes to arrive at school. bill arrives 20 minutes after amy. how much faster (in m/s) is amys average speed for the entire trip? 1 point 1.8 m/s 2.0 m/s 1.5 m/s 2.2 m/s

Explanation:

Step1: Convert distance and time for the car

First, convert 200 km to m and 110 minutes to s. 200 km = 200×1000 = 200000 m, 110 minutes = 110×60 = 6600 s.

Step2: Calculate car's speed

Use the speed formula $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. So the car's speed $v_{car}=\frac{200000}{6600}\approx30.3$ m/s.

Step3: Convert distance and time for Amy

14.4 km = 14.4×1000 = 14400 m, 35 minutes = 35×60 = 2100 s.

Step4: Calculate Amy's speed

Using $v = \frac{d}{t}$, Amy's speed $v_{Amy}=\frac{14400}{2100}=\frac{48}{7}\approx6.86$ m/s.

Step5: Calculate Bill's time

Bill takes 35 + 20= 55 minutes. 55 minutes = 55×60 = 3300 s.

Step6: Calculate Bill's speed

Using $v=\frac{d}{t}$, Bill's speed $v_{Bill}=\frac{14400}{3300}=\frac{48}{11}\approx4.36$ m/s.

Step7: Calculate the difference in speed

The difference in speed $\Delta v=v_{Amy}-v_{Bill}=\frac{48}{7}-\frac{48}{11}=\frac{48\times(11 - 7)}{7\times11}=\frac{48\times4}{77}=\frac{192}{77}\approx2.0$ m/s.

Answer:

2.0 m/s