Question

1. the calculbus and the yammobile are both lined up 10 miles apart at the starting line of a race (thats one long starting line); however, this race is slightly different than most. the calculbus is facing east and will travel straight east while the yammobile is facing west and will travel straight west. at the moment the race begins, the calculbus immediately travels at a constant 80mph while the yammobile immediately travels at a constant 100mph. at what rate is the direct - line distance from the calculbus to the yammobile changing 2 hours into the race?

Explanation:

Step1: Define variables

Let \( x(t) = 80t \) (distance of Calculus east), \( y(t) = 100t \) (distance of Yammobile west). Initial separation: 10 miles. Total horizontal distance: \( D(t) = 10 + x(t) + y(t) \). Direct distance \( s(t) = D(t) = 10 + 180t \) (since they move along a straight line opposite directions).

Step2: Differentiate for rate

\( \frac{ds}{dt} = \frac{d}{dt}(10 + 180t) = 180 \).

Answer:

180 mph