Chapter 6.1, Problem 18E

To determine

The length of the road by averaging the LRAM and RRAM sums.

Answer to Problem 18E

The length of the road is 3665 feet.

Explanation of Solution

Given information:

A companion are driving along the twisty stretch of dirt road in a car whose speedometer works but whose odometer (mileage counter) is broken. The velocity was converted from mi/h to ft/sec using 30 mi/h.

  

Formula used:

The rectangle approximation method is used.

Calculation:

For left hand point rectangle approximation method (LRAM), area is divided into rectangles. Total time is divided into ten equal intervals and at left-hand point of interval calculates the velocity which is equal to height of rectangle then calculates the area of small rectangles then adds all the area. Total area gives the length of road. There is no need to measure height.

  

For right-hand point rectangle approximation method (RRAM), area is divided into rectangles. Total time is divided into ten equal intervals and at right-hand point of interval calculates the velocity which is equal to height of rectangle then calculates the

Area of small rectangles then adds all the area. Total area gives the length of road. There is no need to measure height because we have recorded data.

  

Now, length of road by averaging the LRAM and RRAM sums

  $\begin{array}{l}\text{length}\text{of}\text{road}=\frac{3490+3840}{2}\\ =\frac{7330}{2}\\ \text{length}\text{of}\text{road}=3665\text{feet}\end{array}$

Conclusion:

The length of the road is 3665 feet.