Two boats 100 km horizontally apart travel in opposite directions. Boat 1 travels north at 25 km/h, Boat 2 travels south at 35 km/h. At 4pm, how fast does the distance change between them?
Ok.. I know how to actually solve this, but I'm having trouble understanding what the derivative actually represents. The problem itself says it is "how fast the distance changes between them." The boats are travelling at a constant velocity, so isn't the distance between them changing at the rate of the sum of their velocities?
(d as in distance)
It uses the distance formula.
The derivative comes out to:
4 hours later, the distance changes at 55 km/s, but like I said above, if the boats are traveling at a constant speed, why would there be a difference at any moment of time?