SOLUTION: A truck left city a and b respectively, at the same time traveling toward each other. When they met, the track had traveled 120 more miles than the van. Afterwards, the van travele

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Question 737280: A truck left city a and b respectively, at the same time traveling toward each other. When they met, the track had traveled 120 more miles than the van. Afterwards, the van traveled 9 more hours to reach city B while the truck traveled 4 more hours to reach city A. What is the distance between the 2 cities?
PLEASE HELP!!!!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A van and a truck left city a and b respectively at the same time traveling toward each other.
When they met, the truck had traveled 120 more miles than the van.
Afterwards, the van traveled 9 more hours to reach city B while the truck traveled 4 more hours to reach city A.
What is the distance between the 2 cities?
:
let x = distance from a to meeting point (initially traveled by the van)
then
(x+120) = distance from b to meeting point (initially traveled by the truck)
therefore
(2x+120) = distance from a to b
:
Speed = dist/time
%28x%2B120%29%2F9 = speed of the van traveling to b
x%2F4 = speed of the truck traveling to a
:
Let t = travel time for both to the meeting point (time = dist/speed)
Truck time
%28x%2B120%29%2F%28x%2F4%29 = (x+120)*4%2Fx = %284x%2B480%29%2Fx
Van time
x%2F%28%28x%2B120%29%2F9%29 = x * 9%2F%28x%2B120%29 = %289x%29%2F%28x%2B120%29
Times are equal, therefore
%284x%2B480%29%2Fx = %289x%29%2F%28x%2B120%29
cross multiply
9x^2 = (4x+480)(x+120)
FOIL
9x^2 = 4x^2 + 480x + 480x + 57600
0 = 4x^2 - 9x^2 + 960x + 57600
-5x^2 + 960x + 57600 = 0
simplify, divide by-5
x^2 - 192x - 11520 = 0
Factors to
(x-240)(x+48) = 0
The positive solution
x = 240
a to b distance; 2(240) + 120 = 600 miles
:
:
We can confirm this, find the speed of each
240/4 = 60 km/hr the truck
360/9 = 40 km/hr the van
:
Time to meet point should be the same
truck: 360/60 = 6 hrs
van: 240/40 = 6 hrs