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?
:
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/t}}} = speed of the car
{{{((m+108))/t}}} = speed of the truck
:
Speed should be the same on both parts of the trip, therefore
Car speed:{{{m/t}}} = {{{((m+108))/16}}}
Cross multiply
t(m+108) = 16m
t = {{{(16m)/((m+108))}}}
:
Truck speed:{{{((m+108))/t}}} = {{{m/9}}}
cross multiply
mt = 9(m+108)
mt = 9m + 972
t = {{{((9m+972))/m}}}
:
From the car speed, replace t with {{{(16m)/((m+108))}}}
{{{(16m)/((m+108))}}} = {{{((9m+972))/m}}}
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
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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