Select the correct answerTwo cars A and B travel from one city to another city, at speeds of 60 km/hr and 108 km/hour respectively. If car B takes 2 hours lesser time than car A for the journey, then what is the distance (in km) between the two cities?Options240300330270

To solve this problem, we can use the formula for time, which is distance divided by speed.

Let's denote the distance between the two cities as D (in km), the speed of car A as Sa (in km/hr), the speed of car B as Sb (in km/hr), and the time difference as Δt (in hours).

From the problem, we know that Sa = 60 km/hr, Sb = 108 km/hr, and Δt = 2 hours.

The time it takes for car A to travel from one city to another is D/Sa, and for car B it is D/Sb. According to the problem, the time for car B is 2 hours less than the time for car A, so we can write the equation as follows:

D/Sa - D/Sb = Δt

Substitute the known values into the equation:

D/60 - D/108 = 2

To solve for D, we first need to find a common denominator for the fractions, which is 540. So the equation becomes:

9D/540 - 5D/540 = 2

Simplify the equation:

4D/540 = 2

Multiply both sides of the equation by 540 to solve for D:

4D = 2 * 540

Divide both sides of the equation by 4:

D = 2 * 540 / 4

D = 270

So, the distance between the two cities is 270 km. Therefore, the correct answer is 270.

To solve this problem, we can use the formula for time, which is distance divided by speed.

Let's denote the time it takes for car A to travel between the cities as T (in hours), and the distance between the cities as D (in kilometers).

From the problem, we know that car A travels at 60 km/hr and car B travels at 108 km/hr. We also know that car B takes 2 hours less than car A to travel between the cities.

So we can write down the following two equations based on the formula for time:

D = 60T (equation 1, for car A)

D = 108(T - 2) (equation 2, for car B)

Now we can solve these two equations to find the values of D and T.

First, let's substitute equation 1 into equation 2:

60T = 108(T - 2)

This simplifies to:

60T = 108T - 216

Subtract 108T from both sides:

-48T = -216

Divide both sides by -48:

T = 4.5 hours

Now we can substitute T = 4.5 into equation 1 to find D:

D = 60 * 4.5 = 270 km

So the distance between the two cities is 270 km.

Therefore, the correct answer is 270.