distance word problem

[kris17]

Two city busses leave the terminal at the same time. The first bus drives north at 40 mph, and the second bus drives
east at 30 mph. How fast is the distance between the busses changing after one half hour?
A) 35 mph
B) 50 mph
C) 65 mph
D) 22 mph

Am I supposed to use the rate of change for this one?

 

[JeffM]

How fast is the distance between the busses changing after one half hour?

Am I supposed to use the rate of change for this one?

Isn't the answer to that question rather obvious?

The next question is the rate of change of what?
But that too has a rather obvious answer.

The third question is a bit more subtle. The rate of change with respect to what?

Answer those three questions, and let's move forward from there.

 

[TchrWill]

Two city busses leave the terminal at the same time. The first bus drives north at 40 mph, and the second bus drives
east at 30 mph. How fast is the distance between the busses changing after one half hour?
A) 35 mph
B) 50 mph
C) 65 mph
D) 22 mph

Distance between busses after one hour is sqrt(30^2 + 40^2) = 50 miles
Distance between busses after two hours is 100 miles
Distance between busses after three hours is 150 miles

Thus, ...

 

[HallsofIvy]

Two city busses leave the terminal at the same time. The first bus drives north at 40 mph, and the second bus drives
east at 30 mph. How fast is the distance between the busses changing after one half hour?
A) 35 mph
B) 50 mph
C) 65 mph
D) 22 mph

Am I supposed to use the rate of change for this one?

Yes, "how fast the distance is changing" is a rate of change. Now do you see how the Pythagorean theorem applies here?