A worker reaches his work place 25 minutes late be walking at 6kmph from his house. The next day he increases his speed by 4 kmph and reaches in time. Find the distance from his house to his workplace.
Question
A worker reaches his work place 25 minutes late be walking at 6kmph from his house. The next day he increases his speed by 4 kmph and reaches in time. Find the distance from his house to his workplace.
Solution
Sure, let's solve this step by step:
Step 1: Let's denote the distance between the worker's house and his workplace as 'd' km.
Step 2: The worker initially walks at a speed of 6 km/h. So, the time he takes to reach his workplace is 'd/6' hours.
Step 3: The next day, the worker increases his speed by 4 km/h, making his speed 10 km/h. So, the time he takes this day is 'd/10' hours.
Step 4: According to the problem, the worker is 25 minutes late on the first day. This means that the time he takes on the first day is 25 minutes more than the time he takes on the second day. We can write this as: d/6 = d/10 + 25/60.
Step 5: To solve for 'd', we first need to get rid of the fractions. We can do this by multiplying the entire equation by 60: 10d = 6d + 25.
Step 6: Simplifying this gives us: 4d = 25.
Step 7: Finally, solving for 'd' gives us: d = 25/4 = 6.25 km.
So, the distance from the worker's house to his workplace is 6.25 km.
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