Two 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?Options330270240300
Question
Two 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?Options330270240300
Solution
Let's solve this step by step:
Step 1: Let's denote the distance between the two cities as 'd' km.
Step 2: The time taken by car A to travel this distance at a speed of 60 km/hr is d/60 hours.
Step 3: Similarly, the time taken by car B to travel the same distance at a speed of 108 km/hr is d/108 hours.
Step 4: According to the problem, car B takes 2 hours less than car A to travel the same distance. So, we can write the equation as: (d/60) - (d/108) = 2
Step 5: To solve this equation, first find a common denominator for 60 and 108, which is 540. The equation becomes: (9d/540) - (5d/540) = 2
Step 6: Simplify the equation to get: 4d/540 = 2
Step 7: Solve for 'd' to find the distance between the two cities: d = 2 * 540 / 4 = 270 km
So, the distance between the two cities is 270 km.
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