Mike said, last week I ran 15 miles farther than Bill. Pete said Last week I ran one mile less than 3 times as far as Bill. If Mike and Pete ran the same distance, how far did Bill run?
Bill -- x
mike --- x+15
Pete --- 3x - 1
3x-1 = x+15
2x = 16
x = 8
bill ran 8 miles
check:
Bill -- 8 miles
Mike -- 23 mi
Pet -- 23 mi
Yeah!
thanks
Let's assume the distance Bill ran as "x" miles.
According to Mike, he ran 15 miles farther than Bill. Thus, Mike ran x + 15 miles.
According to Pete, he ran one mile less than 3 times as far as Bill. So, Pete ran 3x - 1 miles.
Given that Mike and Pete ran the same distance, we can set up an equation:
x + 15 = 3x - 1
To solve this equation, we can start by isolating the variable:
x - 3x = -1 - 15
-2x = -16
Next, we can solve for "x" by dividing both sides of the equation by -2:
x = -16 / -2
x = 8
Therefore, Bill ran 8 miles.
To find out how far Bill ran, let's break down the information we have:
- Mike said he ran 15 miles farther than Bill.
- Pete said he ran one mile less than 3 times as far as Bill.
- Mike and Pete ran the same distance.
Let's represent Bill's distance as "x" miles. According to Mike, Mike's distance is 15 miles more than Bill's, so Mike's distance is (x + 15) miles.
According to Pete, Pete's distance is one mile less than 3 times Bill's distance. So Pete's distance is (3x - 1) miles.
Since Mike and Pete ran the same distance, we can set up an equation:
x + 15 = 3x - 1
Now, let's solve for x (Bill's distance):
Subtract x from both sides: 15 = 2x - 1
Add 1 to both sides: 16 = 2x
Divide both sides by 2: x = 8
Therefore, Bill ran 8 miles.