If speed of person is increased by 20% he reaches 15 min early. What is the initial time by the person?

To solve this problem, we need to understand the relationship between speed, time, and distance. The distance remains the same in this problem, but the speed and time change.

1. Let's denote the initial speed as S (km/h) and the initial time as T (hours). Therefore, the distance D can be calculated as D = S * T.

2. According to the problem, the speed increases by 20%, so the new speed is 1.2S. As a result, the time it takes to cover the same distance decreases. Let's denote this new time as T1. So, we have D = 1.2S * T1.

3. From the above two equations, we can conclude that S * T = 1.2S * T1. Simplifying this, we get T = 1.2 * T1.

4. The problem also mentions that the person reaches 15 minutes early. This means that T1 = T - 15/60 (we convert minutes to hours by dividing by 60).

5. Substituting T1 in the equation from step 3, we get T = 1.2 * (T - 15/60).

6. Solving this equation will give us the initial time T.

Let's solve it:

T = 1.2T - 0.3 0.3 = 0.2T T = 0.3 / 0.2 T = 1.5 hours

So, the initial time taken by the person was 1.5 hours.