Ramesh travels by bus from city A to city B at an average speed of 44 km/hr. Suresh travels by taxi from city A to city B at an average speed of 77 km/hr and takes 6 hours lesser than time taken by Ramesh. What is the distance (in km) between the two cities?
Question
Ramesh travels by bus from city A to city B at an average speed of 44 km/hr. Suresh travels by taxi from city A to city B at an average speed of 77 km/hr and takes 6 hours lesser than time taken by Ramesh. What is the distance (in km) between the two cities?
Solution
Let's solve this step by step:
Step 1: Let's denote the time taken by Ramesh to travel from city A to city B as 't' hours. Therefore, the time taken by Suresh would be 't-6' hours (since Suresh takes 6 hours less than Ramesh).
Step 2: We know that distance = speed * time. So, the distance travelled by both Ramesh and Suresh would be the same (since they are travelling between the same two cities).
Step 3: Therefore, we can set up the equation as follows: 44t = 77(t - 6)
Step 4: Solving this equation, we get t = 14 hours. This is the time taken by Ramesh.
Step 5: Now, we can find the distance between the two cities by substituting t = 14 into the equation for distance (distance = speed * time). So, distance = 44 * 14 = 616 km.
Therefore, the distance between city A and city B is 616 km.
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