Chapter 1, Problem 10Q

List assumptions useful to estimate the numbers of car mechanics in (a) San Francisco, (b) your hometown, and then make the estimates.

To determine

The assumptions which are useful to estimate the number of car mechanics in

1. San Francisco
2. Hometown

To Estimate: The number of car mechanics in each.

Answer to Problem 10Q

Solution:

In estimating the number of car mechanics, the assumptions needed are:

1. The population of the city.
2. The number of cars per person in the city (dependent upon the standard of living).
3. The number of cars that a mechanic repairs in a day.
4. The number of workdays in a year.
5. The number of repairs of a car in a year.

1. The number of car mechanics in San Francisco = 1200 mechanics.
2. In hometown, the number of car mechanics = 670 mechanics.

Explanation of Solution

Calculation:

The population of San Francisco 870887 people.

Letthere be 1 car forevery2 people.

A mechanic can repair 3 cars per day.

A mechanic works 260 days per year.

A car needs to be repaired twice per year.

The number of mechanics

  $\text{=}\left(\text{870887}\text{people}\right)\text{×}\left(\frac{\text{1}\text{car}}{\text{2}\text{people}}\right)\text{×}\left(\frac{\text{2}\text{repairs/year}}{\text{1}\text{car}}\right)\text{×}\left(\frac{\text{1year}}{\text{250}\text{workdays}}\right)\text{×}\left(\frac{\text{1mechanic}}{\text{3}\text{repairs}/\text{workday}}\right)$

The number of mechanics (car) =1161 $\approx 1200$ mechanics

The population of hometown $=2\times {10}^6$ people

1car for every 10 people.

A mechanic can repair 2 cars per day.

A mechanic works 300days per year.

A car needs to be repaired twice per year.

The number of mechanics

  $\text{=}\left(2\times {10}^6\text{people}\right)\text{×}\left(\frac{\text{1}\text{car}}{10\text{people}}\right)\text{×}\left(\frac{\text{2}\text{repairs/year}}{\text{car}}\right)\text{×}\left(\frac{\text{1year}}{\text{300}\text{workdays}}\right)\text{×}\left(\frac{\text{1mechanic}}{\text{4}\text{repairs}/\text{workday}}\right)$

  =670 mechanics

Conclusion:

1. The number of car mechanics in San Francisco = 1200 mechanics.
2. In hometown, the number of car mechanics = 670 mechanics.