SOLUTION: A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time. When they met, the truck drove 108 km more than the car. The

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time. When they met, the truck drove 108 km more than the car. The      Log On


   

Question 540853: A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time. When they met, the truck drove 108 km more than the car. The truck took another 9 hours to arrive at city B, and the car took another 16 hours to get to City A. What is the distance between the two cities?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A truck drove from City A to City B, and the car drove from City B to City A on the same road leaving at the same time.
When they met, the truck drove 108 km more than the car.
The truck took another 9 hours to arrive at city B, and the car took another 16 hours to get to City A.
What is the distance between the two cities?
:
See what we can get from the limited information we have.
:
Let m = distance to meeting point driven by the car
then
(m+108) = distance to the meeting point driven by the truck
Then
Distance from A to B = m + m+108
or
2m + 108 = the distance from A to B
:
Let t = travel time of both the truck and the car to the meeting point
Then
m%2Ft = speed of the car
%28%28m%2B108%29%29%2Ft = speed of the truck
:
Speed should be the same on both parts of the trip, therefore
Car speed:m%2Ft = %28%28m%2B108%29%29%2F16
Cross multiply
t(m+108) = 16m
t = %2816m%29%2F%28%28m%2B108%29%29
:
Truck speed:%28%28m%2B108%29%29%2Ft = m%2F9
cross multiply
mt = 9(m+108)
mt = 9m + 972
t = %28%289m%2B972%29%29%2Fm
:
From the car speed, replace t with %2816m%29%2F%28%28m%2B108%29%29
%2816m%29%2F%28%28m%2B108%29%29 = %28%289m%2B972%29%29%2Fm
Cross multiply
(m+108)(9m+972) = 16m^2
Foil
9m^2 + 972m + 972m + 104976 = 16m^2
-16m^2 + 9m^2 + 1944m + 104976 = 0
-7m^2 + 1944m + 104976 = 0
:
Solve this quadratic equation with the quadratic formula:
the positive solution is what we want
m = 324 km
:
Then dist of A to B 2m+108, therefore:
2(324) + 108 = 756 km
:
:
We can confirm this solution by finding the speed of the car of the truck then finding the time
truck:
324/9 = 36 mph
Car
(324+108)/16 = 27 mph
Find the total travel time of each
756/27 = 28 hrs
756/36 = 21 hrs
----------------
time dif: 7 hrs as given (16-9)
:
A lot of steps here, hopefully you follow the steps and it will make sense to you. Let me know please. C