I walk at 4 kilometers per hour and run at 6 kilometers per hour. I find I can save 3 minutes and 45 seconds by running instead of walking to school in the morning. How far do I live from school?

To find the distance to school, calculate the time difference saved by running and use it to determine the distance using the given speeds. In this case, the student lives 3 km away from school.

Explanation:

To find the distance from school:

First, determine the time difference saved by running: 3 minutes 45 seconds = ((3 60) + 45) seconds = 225 seconds.
Next, calculate the distance using the time and speeds: Let the distance to school be D km.
Walking time = D / 4 hours = D 60 / 4 minutes = 15 D minutes.
Running time = D / 6 hours = D 60 / 6 minutes = 10 D minutes.
Equation: 15D - 10*D = 225 seconds.
Solve the equation to find D = 3 km.

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