SOLUTION: 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
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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? Leave your answer in decimal hours. Show the setup that supports your answer. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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 results: 299.967 ~ 300
