word problem

Question

Roger has a house in telluride, Colorado, but starts a new job in Denver. Every Monday, he drives his car 332 miles from Telluride to Denver, spends the week in a company apartment, and then drives back to Telluride on Friday. He doesn’t use his car for anything else. After 20 weeks of this, his odometer shows that he has travelled 240,218 miles since he bought the car. Write a linear model which gives the odometer reading of the car as a function of the number of weeks since Roger started the new job.

Answer 1

We need a linear model. So, start with y=mx+b, where y = number of miles on odometer and x = number of weeks since starting job.

 

First, we find the slope m. We know m = change in y / change in x = change in miles / change in weeks. If change in weeks is 1, we know the change in miles is 332*2 (driving to and from Denver in any given week). So, m = 332 * 2 / 1 = 664. So far our model is y=664x + b. 

 

Next, we use the remaining given information to solve for b. The problem tells us that after 20 weeks, the odometer reads 240,218. So, we have:

 

240,218 = 664*20 + b

 

which yields the solution b = 226,938. Our model is:

 

y = 664x + 226938

 

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