# I need help with a math problem for a group project in my classAndrew has been driving toward home at a constant speed. After two hours, he is 100 miles from home.  After three and a half hours,...

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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