Calculus
posted by Katie .
Two trucks start from the same point. One truck travels due east at a rate of 50 mph and the other trucks travels due north at a rate of 60 mph. At what rate is the distance between the two vehicles increasing 1 1/2 hours later?
I think the answer is 55 mph because I added 60 + 55 and divided by 2 and got 55 mph.

Calculus 
Damon
Oh my :(
The distance between them is the hypotenuse of a right triangle.
D^2 = x^2 + y^2
where
x = 50 t
y = 60 t
so
D^2 = 2500 t^2 + 3600 t^2 = 6100 t^2
now take time derivative
2 D dD/dt = 12200 t
at t = 1.5
D^2 = 6100 (2.25)
D = 117 miles
2 D = 234.3 miles
so
dD/dt = 12200(1.5)/234.3 = 78.1 miles/hour
Respond to this Question
Similar Questions

Math
A car is heading east toward an intersection at the rate of 40 mph. A truck is heading south, away from the same intersection at the rate of 60 mph. At what rate is the distance between the car and the truck changing when the car is … 
Math
A car is heading east toward an intersection at the rate of 40 mph. A truck is heading south, away from the same intersection at the rate of 60 mph. At what rate is the distance between the car and the truck changing when the car is … 
calculus
Two cars start moving from the same point. One travels south at 28mi/h and the other travels west at 50mi/h. At what rate is the distance between the cars increasing 4 hours later? 
calculus
Two cars start from the same point at the same time. One travels north at 25 mph, and the other travels east at 60 mph. How fast is the distance between them increasing at the end of 1 hr? 
calculas maths
.Two hikers begin at the same location and walk in perpendicular directions. Hiker A travels due north at a rate of 3 miles per hour; Hiker B travels due east at a rate of 5 miles per hour. At what rate is the distance between the … 
math
Can you check my answer to see if i really get this word problem thing A camper leaves the campsite walking due east at a rate of 3.5 mph. Another camper leaves the campsite at the same time but travels due west. In two hours the campers … 
Calculus
Two cars start moving from the same point. One travels south at 60 mph and the other travels west at 25 mph. At what rate is the distance between the cars increasing 2 hours later? 
Math
Two cyclists leave from an intersection at the same time. One travels due north at a speed of 18mph, and the other travels due east at 24mph. how long until the distance between them is 150 miles? 
math
Two trains leave a station at 11:00am. One train travels north at a rate of 75 mph and another travels east at a rate of 60 mph. Assuming the trains do not stop, about how many minutes will it take for the trains to be 250 miles apart? 
Calculus
Two planes leave an airport simultaneously. One travels north at 300 mph and the other travels west at 400 mph. How fast is the distance between them changing after 10 minutes?