Answer:
a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.
b)  Average speed of car is 84 km/h
Step-by-step explanation:
A -----------------------z------------B
           <u>Left</u>      <u>Speed(km/h)</u>      <u>Time</u>
Car:   12PM            X   
Van:   12PM           60
Car/Van
DistanceCar        AB + z
DistanceVan       Az
Ratio:                  (AB+z)/Az  = 7/5
Time until both meet = T (in hours)
Distance Car:            xT
Distance Van:           60T
====
   xT = AB + z
   60T = Az
---
(xT/60T)= (7/5)
x = 60(7/5)
x = 84 km/h
=====
Time for car to reach B is:    time (hr) = 108 km/(84 km/h)
                                                  time = 1.286 hours
Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)
                                                    distance = 77.14 km
At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.
Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.
Car Distance + Van Distance = 30.86 km
T(84 km/h) + t(60 km)
They meet when they are 0 km apart, which can be modeled with the following equation:
Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.
Let <u>t</u> be the time <u>after</u> 1.286 hours that both vehicles meet/collide.
t*(60 km/h)  +  t(84 km/h) = 30.86 km
t(60+84) = 30.86 km
t(144 km/h) = 30.86 km
t = 0.2143 hr
Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.
=================
a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.
b)  Average speed of car is 84 km/h
==============
<u>CHECK</u>
Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?
Car distance is (1.5 hr)(84 km/h) = 126 km
Van distance is (1.5 hr)(60 km/h) = 90.0 km
Ratio is 126/90 or 1.4
Ratio of 7/5 is 1.4
<u><em>YES</em></u>