# Thread: Stuck on Related Rate question

1. ## Stuck on Related Rate question

At noon, ship A passes the point P that is 8 km west of a harbour, heading due south at 10 km/h. At 9 a.m., ship B had left the harbour, sailing due south at 6 km/h.

Give an expression for dA, the distance between ship A and the point P, in terms of t, the number of hours after noon.

I got dA = 10t km

Give an expression for dB, the distance between ship B and the harbour, in terms of t, the number of hours after noon.
I got dB= 6(t+3) km
Give an expression for D, the distance between the two ships, in terms of t, the number of hours after noon.

I got D = sqrt(136t^2+216t+324)

by using Pythagoras D^2 = (10t)^2(6t+18)^2

Somehow this is not coming out correctly? Any suggestions? Can it be simplified further?

Any help would be wonderful, cheers

2. Originally Posted by youmuggles
At noon, ship A passes the point P that is 8 km west of a harbour, heading due south at 10 km/h. At 9 a.m., ship B had left the harbour, sailing due south at 6 km/h.

Give an expression for dA, the distance between ship A and the point P, in terms of t, the number of hours after noon.

I got dA = 10t km

Give an expression for dB, the distance between ship B and the harbour, in terms of t, the number of hours after noon.
I got dB= 6(t+3) km
Give an expression for D, the distance between the two ships, in terms of t, the number of hours after noon.

I got D = sqrt(136t^2+216t+324)

by using Pythagoras D^2 = (10t)^2(6t+18)^2

Somehow this is not coming out correctly? Any suggestions? Can it be simplified further?

Any help would be wonderful, cheers
east-west distance between the two ships at any time t = 8 km

north-south distance between the two ships at any time t in km ...

$\displaystyle |10t - 6(t+3)| = |4t - 18|$

$\displaystyle D = \sqrt{8^2 + (4t - 18)^2}$