Boat A and B leave the same place at the same time. A heads north at 12km/hr. B heads east at 18km.hr.......?

Question

After 2.5 hours, how fast is the distance between them increasing (in km/hr)

Answer 1

You have the answer at the distance between them after 2.5 hours of travel, but your question is how fast the distance is increasing.

Divide your answer by 2.5, or time traveled to get the correct answer.

Answer 2

Hi

   Just divide the 54.o83269 by 2.5 (hrs travelled)

   = 21.633

Answer 3

54.08 Kilometers

Answer 4

Let's see ...

Let dA/dt = 12, dB/dt = 18.

After 2.5 hours, A has traveled 30 km, and B has traveled 45 km. By the Pythagorean Theorem, the distance between them is sqrt(2925).

A^2 + B^2 = D^2, where d is the distance between them.

2A*dA/dt + 2B*dB/dt = 2D*dD/dt

2(30)*12 + 2*45*18 = 2*sqrt(2925)*dD/dt

2340 = 2sqrt(2925)*dD/dt

1170 = sqrt(2925) * dD/dt

1170 = 15sqrt13* dD/dt

1170/(15sqrt13) = dD/dt

78(sqrt 13)/13 = dD/dt

The distance between them is increasing

78(sqrt13)/13 = 21.633 km/hr