Three out of every four trucks on the road are followed by a

Three out of every four trucks on the road are followed by a car, while only one out of every five cars are followed by a truck. What fraction of vehicles on the road are trucks?

Please help! and explain not sure where to start

Solution

P(car after a truck) =3/4= 0.75
P(truck after a car)= 1/5 = 0.2

fraction of vehicles on road to be truck=?

let there be 100 vehicles on the road
cars=x, trucks =100-x

so, 0.75*(100-x) =x1      -(1)
      0.2*x2=100-x            -(2)

and x1+ x2=x                    

solving 1 and 2 ,we get

       75=1.75*x1+0.75*x2      -(3)
       100=x1 + 1.2 *x2             - (4)
multiply 4 by 1.75
        75=1.75*x1+0.75*x2   
       175=1.75x1 + 2.1 *x2
thus, 100 = 1.35*x2
x2= 74.074
x1= 11.11115
hence, x= 85 (approx)
       thus fraction of vehicles on road to be cars= 85/100 = 0.85
fraction of vehicles on road to be trucks= 15/100 = 0.15