Question

Pablo is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Pablo has 67 miles to his destination after 49 minutes of driving, and he has 47.5 miles to his destination after 75 minutes of driving. How many miles will he have to his destination after 85 minutes of driving?

Answer 1

40 miles to his destination.

Explanation:

If the distance to the destination is a linear function of his driving time then the function f(x) has the form f(x)=mx + b

Now we're going to write two equations with the data that was given to us to find the function for this problem:

`67=49m+b\\47.5=75m+b\\\\67-49m=b\\47.5-75m=b\\\\67-49m=47.5-75m\\-49m+75m=47.5-67\\26m=-19.5\\m=-0.75\\\\b=67-49m\\b=67-49(-0.75)\\b=67+36.75\\b=103.75`

Therefore the equation f(x), is f(x) = -0.75x+103.75

To find how many miles he will have after driving 85 minutes:

`f(85)=-0.75(85)+103.75\\f(85)=-63.75+103.75\\f(85)=40`

He will have 40 miles to his destination