Question

Suppose a person wants to travel d miles at a constant speed of left parenthesis 60 plus x right parenthesis(60+x) ​mi/hr, where x could be positive or negative. the time in minutes required to travel d miles is upper t left parenthesis x right parenthesis equals 60 upper d left parenthesis 60 plus x right parenthesis superscript negative 1t(x)=60d(60+x)−1.
a. given the linear approximation to t at the point xequals=0 is upper t left parenthesis x right parenthesis almost equals upper l left parenthesis x right parenthesis equals upper d left parenthesis 1 minus startfraction x over 60 endfraction right parenthesist(x)≈l(x)=d1− x 60​, approximate the amount of time it takes to drive 8484 miles at 6262 ​mi/hr.
b. what is the exact time​ required?

Answer 1

A) We can use the linear approximation to estimate the amount of time it takes. We're given that the linear approximation to t at the point x = 0 is t(x) ≈ L(x) = d(1–(x/60)). If it drives 84 miles at 62 mi/hr, we'll plug 84 in for d and 62 – 60 = 2 in for x to approximate the amount of time it takes.

L(2) = 84(1 – 2/60) = 81.2 minutes

So the answer for part a is 81.2 minutes.

b) Exact time = Distance/Speed = 84/62 = 1.35 hours, which is equivalent to 1.35 * 60 = 81.3 minutes.