SOLUTION: Car A is currently 80 km south of a perpendicular intersection with an east-west road. Car B is on the east-west road, 260 km west of the same intersection. Car A is travelling nor

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Car A is currently 80 km south of a perpendicular intersection with an east-west road. Car B is on the east-west road, 260 km west of the same intersection. Car A is travelling nor      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 317526: Car A is currently 80 km south of a perpendicular intersection with an east-west road. Car B is on the east-west road, 260 km west of the same intersection. Car A is travelling north at 80 km/h; Car B is travelling east at 100 km/h. Assuming that the cars will continue in a straight line with constant velocities, after 2 hours how fast is the distance between the two cars changing?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call A, the distance from the intersection to car A.
Let's call B, the distance from the intersection to car B.
The distance between the cars is D.
A and B form a right triangle with D as the hypotenuse.
D%5E2=A%5E2%2BB%5E2
If you differentiate with respect to time,
2D%2A%28dD%2Fdt%29=2A%2A%28dA%2Fdt%29%2B2B%2A%28dB%2Fdt%29
After 2 hours,
A=-80%2B80%2A2=80
B=-260%2B100%2A2=-60
dA%2Fdt=80
dB%2Fdt=100
D%5E2=A%5E2%2BB%5E2=80%5E2%2B60%5E2=100%5E2
D=100
.
.
.
2D%2AdD%2Fdt=2A%2AdA%2Fdt%2B2%2AB%2AdB%2Fdt
2%28100%29dD%2Fdt=2%2A80%2A80%2B2%28-60%29%2880%29
200%2AdD%2Fdt=2%2880%29%2880-60%29=3200
dD%2Fdt=3200%2F200
dD%2Fdt=16
.
.
.
The only issue remaining is the sign of the rate of change.
Distance A is growing while Distance B is diminishing (A is growing slower than B).
Distance D is therefore diminishing.
highlight%28dD%2Fdt=-16%29 km/h