Uhh, is it because they have the greatest distance when both their velocities are the same because Person A had traveled at a higher velocity than Person B and thus traveled a greater distance that added up the most at the end of their walk?
I used the first derivative test and at t = 1.5 got a positive result and at t = 1.7 got a negative one so that means at t = 1.60944 there is a maximum on the original function. Do you think that's enough to show why the greatest distance between the two walkers is at t = 1.60944?
Alright, so I'm not sure if I'm reading what you wrote correctly but basically i had
(1 - e-t) - 0.2(et - 1) = 0
to find the critical points.
I get t = 0 and t = 1.60944.
So I'm guessing it's at t = 1.60944?
Homework Statement
Two walkers start at the same time from the same place and travel in the same direction with velocities given by
A(t) = 1 - e-t miles per minute and B(t) = 0.2(et - 1) miles per minute and t > 0. They travel until they have the same velocity.
At what time is the distance...