Suppose a person wants to travel Dmiles at a constant speed

Suppose a person wants to travel D-miles at a constant speed of (60+x)mi/hr, where x could be positive or negative. The time in minutes required to travel D miles is t(x)=60D(60+x)^-1.

A. Given the linear approximation to T at the point x=0 is T(x)=L(x)=D(1-(x/60)), approximate the amount of time it takes to drive 85 miles at 58 mi/hr. (in minutes)

B. What is the exact time required?

Solution

A) t(x) = 60D/(60 +x)

Applying Linear approximation : t(x) = 60D/60( 1+x/60)

= D/(1+x/60) = D(1+x/60)^-1 = D(1 -x/60)

Now for D = 85mi and x = 58 mi/hr

T(x) = 85( 1- 58/80) = 2.833 hr = 170 min

B) for exact time use :t(x) = 60D/(60 +x)

T = 60*85/( 60 +58) = 5100/118 = 43.22 hr