Question 821859
Two trucks leave the same loading dock at different times.
 Track A leaves a noon and drives due north at 40 mph.
 Truck B leaves at 1:00 and drives due east at 45 mph.
 At what time of the day will the trucks be exactly 300 miles apart?
:
Let t = travel time Truck B
then
(t+1) = travel time for Truck A
therefore
40(t+1) = dist traveled by A
45t = dist traveled by B
:
This is a pythag problem, the hypotenuse = 300 mi
:
[40(t+1)]^2 + (45t)^2 = 300^2
(40t+40)^2 + (45t)^2 = 90000
FOIL (40t+40)(40t+40)
1600t^2 + 1600t + 1600t + 1600 + 2025t^2 = 90000
Combine like terms
3625t^2 + 3200t + 1600 - 90000 = 0
3625t^2 + 3200 - 88400 = 0
Simplify, divide by 25
145t^2 + 128t - 3536 = 0
Using the quadratic formula, I got a positive solution of
t = 4.516 hrs travel time of Truck B
then, obviously:
5.516 hrs for truck A
:
Find the time of day:
 12:00 + 5 + (.516(60)) = 5:31 PM when they are 300 mi apart 
:
:
Check this in your calc, enter {{{sqrt((5.516*40)^2 + (4.516*45)^2)}}} results: 299.967 ~ 300