I need help with a math problem for a group project in my class
Andrew has been driving toward home at a constant speed. After two hours, he is 100 miles from home. After three and a half hours, he is 25 miles from home.
How far from home was Andrew when he started driving?
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Let x represent the distance between the starting point and home. Since the speed is constant, 2 hours times the speed in miles per hour will result in the miles traveled. Let s = speed. One equation for traveling 2 hours is: 2s=x-100. The distance is x-100 due to Andrew still being 100 miles from home.
The other equation for traveling 3.5 hours is: 3.5s=x-25. The distance is x-25 due to Andrew being 25 miles from home after 3.5 miles.
With two equations to work with: 2s=x-100 and 3.5s=x-25.
Solving the first equation for s: s=(x-100)/2 = (x/2) - 50.
Substitute x/2 - 50 for s in the second equation:
3.5(x/2 - 50) = x-25
1.75x - 175 = x - 25
Subtract x from both sides: .75x - 175 = -25
Add 175 to both sides: .75x = 150
Divide by .75 on both sides: x = 200
Andrew was 200 miles from home when he started driving.
To find his speed or rate, 2s = 200 - 100
2s = 100
s = 50
Andrew's constant rate is 50 miles per hour.
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