Carrie and Crystal live at a equal distances from school. Carries walks to school at an average rate of 3 miles per hour and Crystal rides her bike at an avergae rate of 9 miles per hour. It takes Carrie 20 minutes longer than Crystal to get to school. How far do Crystal and Carrie live?
distanceCarrie=3mi/hr*time
distanceCrystal=9mi/hr*(time-1/3) 20 min is 1/3 of an hr...
set them equal
3t=9t-3
t= 1/2 hr
now you can figure the distance from the first equation.
To find the distance that Carrie and Crystal live from school, we first need to determine the time it takes for each of them to get to school.
Let's assume the distance from Carrie and Crystal's houses to school is "d" miles.
Carrie walks to school at a rate of 3 miles per hour. Let's denote the time it takes for Carrie to get to school as "t" (in hours).
Therefore, we can write the equation: d = 3t
Crystal rides her bike to school at a rate of 9 miles per hour. Since the distance is the same, let's denote the time it takes for Crystal to get to school as "t - 20/60" (in hours). The 20 minutes need to be converted to hours by dividing by 60.
Therefore, we can write the equation: d = 9(t - 20/60)
Now, we can set the two equations equal to each other and solve for "t":
3t = 9(t - 20/60)
To simplify the equation, let's convert 20 minutes to hours: 20/60 = 1/3
3t = 9(t - 1/3)
3t = 9t - 3
3 = 9t - 3t
3 = 6t
t = 3/6
t = 1/2
Now that we have found "t," we can substitute it into either equation to find the distance:
d = 3t
d = 3 * (1/2)
d = 3/2
d = 1.5 miles
Thus, Crystal and Carrie live at a distance of 1.5 miles from school.