How Fast is the Distance Between Two Cars Changing After 4 Hours?

[Stanc]

Homework Statement

Car 1 is 148 km north of Car 2. Car 1 moves east at 24km/h while Car 2 moves north at 19 km/h. What rate is the distance between them changing after 4 hours?

The Attempt at a Solution

Here is What I did:

By the Pythagorean Theorem,
d^2 = y^2 + x^2
d/dt(d^2) = d/dt(y^2 + x^2)
2d(dd/dt) = 2y(dy/dt) + 2x(dx/dt)
At 4 hours, y = 148 + 4(19) = 148 + 76 = 224, x = 4(24) = 96, and d = (224^2 + 96^2)^(1/2) = 243.7
Substitute 224 for y, 96 for x, 19 for dy/dt, 24 for dx/dt, and 243.7 for d, and solve for dd/dt.
2(243.7)dd/dt = 2(224)19 + 2(96)24
dd/dt = 26.9 km/hrMy question is the bolded part: should I be subtracting the 76km car 2 travels in 4 hours from 148km or adding it like I did?

 

[chiro]

Hey Stanc.

Since Car 2 is -148 km north (+148km south) then the square distance in terms of the y co-ordinate should be (-148 + 4 x 19)^2.