Question

Give an answer is explanation ​

Answer 1

Given Question

A car covers the distance between two cities in 6 hours. A van covers the same distance in 5.5 hours by travelling 4km/hr faster than car. What is the distance between the two cities? Find the speeds of the car and van.

$\large\underline{\sf{Solution-}}$

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

$\rm :\longmapsto\:\boxed{\tt{ y = 6x}} - - - - (1)$

➢ Also, Distance (y) covered by van at the speed of x + 4 km per hour in 5.5 hours is

$\rm :\longmapsto\:\boxed{\tt{ y = 5.5(x + 4)}} - - - - (2)$

So, from equation (1) and (2), we have

$\rm :\longmapsto\:6x = 5.5(x + 4)$

$\rm :\longmapsto\:6x = 5.5x + 22$

$\rm :\longmapsto\:6x - 5.5x = 22$

$\rm :\longmapsto\:0.5x = 22$

$\rm :\longmapsto\:\dfrac{5}{10} \times x = 22$

$\rm :\longmapsto\:\dfrac{1}{2} \times x = 22$

$\bf\implies \:x = 44$

On substituting the value of x, in equation (1), we have

$\rm :\longmapsto\:y = 6 \times 44$

$\bf\implies \:y = 264$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Distance \: between \: cities = 264 \: km} \\ \\ &\sf{Speed \: of \: car \: = \: 44 \: km \: per \: hour}\\ \\ &\sf{Speed \: of \: van \: = \: 48 \: km \: per \: hour} \end{cases}\end{gathered}\end{gathered}$

Answer 2

Answer:

Given Question

A car covers the distance between two cities in 6 hours. A van covers the same distance in 5.5 hours by travelling 4km/hr faster than car. What is the distance between the two cities? Find the speeds of the car and van.

$\large\underline{\sf{Solution-}}$

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

$\rm :\longmapsto\:\boxed{\tt{ y = 6x}} - - - - (1)$

➢ Also, Distance (y) covered by van at the speed of x + 4 km per hour in 5.5 hours is

$\rm :\longmapsto\:\boxed{\tt{ y = 5.5(x + 4)}} - - - - (2)$

So, from equation (1) and (2), we have

$\rm :\longmapsto\:6x = 5.5(x + 4)$

$\rm :\longmapsto\:6x = 5.5x + 22$

$\rm :\longmapsto\:6x - 5.5x = 22$

$\rm :\longmapsto\:0.5x = 22$

$\rm :\longmapsto\:\dfrac{5}{10} \times x = 22$

$\rm :\longmapsto\:\dfrac{1}{2} \times x = 22$

$\bf\implies \:x = 44$

On substituting the value of x, in equation (1), we have

$\rm :\longmapsto\:y = 6 \times 44$

$\bf\implies \:y = 264$

So,

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Distance \: between \: cities = 264 \: km} \\ \\ &\sf{Speed \: of \: car \: = \: 44 \: km \: per \: hour}\\ \\ &\sf{Speed \: of \: van \: = \: 48 \: km \: per \: hour} \end{cases}\end{gathered}\end{gathered}$