#### To determine

**To use:**

The midpoint rule to estimate the distance between the two cars

#### Answer

145 miles

#### Explanation

**1) Concept:**

The area under the velocity curve represents the distance traveled by the car.

Use the midpoint rule to evaluate the area.

**2) Midpoint rule**

∫abfx dx=∑i=1nfxi∆x= ∆x ( f(x1)+fx2+…+f xn)

where ∆x= b-an and xi is a midpoint of [xi-1 , xi]

**3) Given:**

The table that shows velocities of each car (in miles per hour)

**4) Calculation:**

The area under the velocity curve represents the distance traveled by the car.

The difference of the areas under the curves is thedistance between the cars after 10 seconds.

So we calculate Vk-Vc.

With this data, we can take n = 5, and use the midpoint rule.

To find ∆t, convert time in hours.

1 second=13600 hours

10 sec =1360h

∆t=1360-05 =11800

Midpoints of the intervals are t1=1, t2=3, t3=5, t4=7, t5=9

Distance kelly - Distancechris= ∫01/360Vk dt-∫01/360 Vcdt=∫01/360(Vk- Vc) dt∫01/360(Vk- Vc) dt= ∆t ( 2+6+9+11+12)

=118002+6+9+11+12

=1180040

=145miles

**Conclusion:**

Kelly is

145 miles

farther than Chris.