Amy leaves home at the same time every morning and gets to school exactly at 8 AM. If she traveled at 70 meters per minute she would arrive 10 minutes early. If she traveled at 60 meters per minute she would arrive 8 minutes early. What time does Amy leave home each morning?
If she travels x minutes at 70m/min, then the distance is 70x meters. It takes her 2 minutes longer at 60m/min.
70x = 60(x+2)
x = 12
So, the distance is 840 meters.
Her normal speed takes her 22 minutes, so she leaves at 7:38
To determine what time Amy leaves home each morning, we need to analyze the information given.
Let's start by assuming that Amy travels at a certain speed, denoted as v meters per minute. According to the problem, we know that if she traveled at 70 meters per minute, she would arrive 10 minutes early, and if she traveled at 60 meters per minute, she would arrive 8 minutes early.
Let's denote the time she takes to travel as t minutes. We can use the formula distance = speed × time to find the distance between her home and school.
At a speed of 70 meters per minute, the distance between her home and school is d1 = 70 × (t - 10) meters, since she arrives 10 minutes early.
At a speed of 60 meters per minute, the distance between her home and school is d2 = 60 × (t - 8) meters, since she arrives 8 minutes early.
Since both distances represent the same home-to-school distance, we can set them equal to each other: d1 = d2.
70 × (t - 10) = 60 × (t - 8)
Now let's solve this equation to find the value of t.
70t - 700 = 60t - 480
10t = 220
t = 22
So, it takes Amy 22 minutes to travel from home to school.
To find out what time she leaves home, we need to subtract 22 minutes from her school arrival time of 8 AM.
8:00 AM - 22 minutes = 7:38 AM
Therefore, Amy leaves home at 7:38 AM each morning.