Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A car covers the distance between two cities in 6 hours.
A van covers the same distance in 5.5 hours.
The speed of the van is 4 km per hour faster than the speed of car.
Let assume that
Speed of the car be x km per hour
So,
Speed of van is x + 4 km per hour.
Let further assume that
Distance between two cities be y km.
We know, Distance covered = Speed × Time.
➢ Now, Distance (y) covered by car at the speed of x km per hour in 6 hours is
[tex]\rm :\longmapsto\:\boxed{\tt{ y = 6x}} - - - - (1)[/tex]
➢ Also, Distance (y) covered by van at the speed of x + 4 km per hour in 5.5 hours is
[tex]\rm :\longmapsto\:\boxed{\tt{ y = 5.5(x + 4)}} - - - - (2)[/tex]
So, from equation (1) and (2), we have
[tex]\rm :\longmapsto\:6x = 5.5(x + 4)[/tex]
[tex]\rm :\longmapsto\:6x = 5.5x + 22[/tex]
[tex]\rm :\longmapsto\:6x - 5.5x = 22[/tex]
[tex]\rm :\longmapsto\:0.5x = 22[/tex]
[tex]\rm :\longmapsto\:\dfrac{5}{10} \times x = 22[/tex]
[tex]\rm :\longmapsto\:\dfrac{1}{2} \times x = 22[/tex]
[tex]\bf\implies \:x = 44[/tex]
On substituting the value of x, in equation (1), we have
[tex]\rm :\longmapsto\:y = 6 \times 44[/tex]
[tex]\bf\implies \:y = 264[/tex]
So,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Distance \: between \: cities = 264 \: km} \\ \\ &\sf{Speed \: of \: car \: = \: 44 \: km \: per \: hour}\\ \\ &\sf{Speed \: of \: van \: = \: 48 \: km \: per \: hour} \end{cases}\end{gathered}\end{gathered}[/tex]
