Johnny's home is m miles from school. Johnny runs to school at a speed of 8 mph and then walks home from school at half that speed. Suppose it takes Johnny 15 minutes longer to walk home than to run to school. Write an equation that shows this relationship.
Let's use the equation d = rt, where d is the distance, r is the rate, and t is the time.
The time it takes Johnny to run to school at 8 mph is: t1 = d/8.
The time it takes Johnny to walk home from school at half that speed (4 mph) is: t2 = d/4.
Since it takes him 15 minutes longer to walk home than to run to school, we can add 15 minutes (or 15/60 hours) to t1: t1 + 15/60.
The equation that shows this relationship is:
t2 = t1 + 15/60.
Substituting the values of t2 and t1 into the equation, we have:
d/4 = d/8 + 15/60.
This is the equation that represents the relationship between the distances, rates, and times.