A Mathematician needed URGENTLY PLEASE :(?

Question

i have a related rates question and i do not understand this...please help...

Joe is driving west at 60km/h and Dave is driving south at 70km/h both cars are approaching the intersection of the two roads. At what rate is the distance between the cars decreasing when Joe's car os 0.4 and Dave is 0.3 km form the intersection?

Please help I've been stuck on this for awhile :(

Answer 1

Take the intersection as (0,0)
The coordinates of J are( 0,4-60t,0) and those of D(0,0.3-70t)
D=sqrt (0,4-60t)^2+(0,3 -70t)^2
D´= 1/sqrt() ( -120(0.4-60t)-140(0.3-70t))At t= 0
dD/dt= 1/sqrt( 0.25) *(-120) = -60 km/h
So the distance is decreasing at a rate of 60km/h

Answer 2

I think you are looking at 90 km/hr.
Try drawing it out on paper and make a triangle from the intersection, connecting the two cars. Calculate the angle between the direction of travel and the direction of the other car. Now, break down the velocities (using triangle geometry again) into two components - one towards the other car, and one at right angles to this direction. I think you'll see that the left car is approaching the right one at 48 km/hr, while the right one is approaching the left one at 42 km/hr... giving you a 90 km/hr total.