SOLUTION: At 1:00 pm, a freight truck left P to Q and at 2:15 pm a car left Q for P, both traveling at uniform rates. The two vehicles passed each other on the way at 6:20 pm. If they arrive

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Question 483602: At 1:00 pm, a freight truck left P to Q and at 2:15 pm a car left Q for P, both traveling at uniform rates. The two vehicles passed each other on the way at 6:20 pm. If they arrived at their destinations at the same time, what that time?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
At 1:00 pm, a freight truck left P to Q and at 2:15 pm a car left Q for P, both traveling at uniform rates.
The two vehicles passed each other on the way at 6:20 pm.
If they arrived at their destinations at the same time, what that time?
:
Let t = time for the car to go from q to p
then
(t+1.25) = time for truck to go from p to q
:
Let x = truck speed
Let y = car speed
:
We can establish a relationship between x and y, write a distance equation
Truck dist = car dist
x(t+1.25) = yt
x = %28yt%29%2F%28t%2B1.25%29
:
6:20 - 2:15 = 4 hrs 5 min travel time for the car when they meet
6:20 = 1:00 = 5 hrs 20 min travel time for the truck when they meet
:
yt = total distance (from p to q)
:
Change:
4 hrs 5 min to 4.083 hrs
5 hrs 20 min to 5.333 hrs
:
When they meet:
truck dist + car dist = total dist
5.333x + 4.083y = yt
:
Replace x with %28yt%29%2F%28t%2B1.25%29
5.333(%28yt%29%2F%28t%2B1.25%29) + 4.083y = yt
:
%285.333yt%29%2F%28t%2B1.25%29 + 4.083y = yt
:
divide thru by y
%285.333t%29%2F%28t%2B1.25%29 + 4.083 = t
:
Multiply by (t+1.25), results
5.333t + 4.083(t+1.25) = t(t+1.25)
5.333t + 4.083t + 5.1 = t^2 + 1.25t
9.416t + 5.1 = t^2 + 1.25t
Combine like terms
t^2 + 1.25t - 9.416t - 5.1 = 0
A quadratic equation
t^2 - 8.166t - 5.1 = 0
Using the quadratic formula, the positive solution
t ~ 8.75 hrs which is 8 hrs 45 min
:
Car arrives 2:15 + 8.45 = 11:00
Truck arrives: 1:00 + 1.15 + 8.45 = 11:00
;
:
Can we prove this? assign the car a speed of 60 mph
Find the speed of the truck using
x = %28yt%29%2F%28t%2B1.25%29
x = %2860%2A8.75%29%2F%288.75%2B1.25%29
x = %28525%29%2F10
x = 52.5 mph is the truck
:
When meet they should have traveled the total dist
5.333(52.5) ~ 280 mi, truck
4.083(60) ~ 245 mi
---------------------
total dist: 525 mi
:
Which agrees with the total dist: 60*8.75 = 525 mi
:
Summarize: Truck arrives at q and car arrives at p at 11:00 pm