Give the answed of the question Doreen ran 4 miles farther than ludy. Together, they ran a distance of 20 miles.How far did each ran?

Runners: Lucy--> L =

Doreen -->D = L+4
Total miles ran is 20--> 20 = L + D
20 = L + L + 4
20-4 = 2L
16 = 2L
8 = L -> L = 8 mi.
D = L + 4 = 12 mi.
Double Check: 20 = L + D
20 = 8 + 12

To solve this problem, we can use a system of equations. Let's assign variables to the distances each person ran:

Let's say Doreen ran x miles and Ludy ran y miles.

According to the problem statement, Doreen ran 4 miles farther than Ludy. Therefore, we can express their distances in terms of x and y as:

Doreen's distance: x = y + 4
Ludy's distance: y = y

The problem also states that together, they ran a total distance of 20 miles. So we can express this as an equation:

x + y = 20

Now we have a system of two equations:

x = y + 4
x + y = 20

To solve this system, we can substitute the value of x from the first equation into the second equation:

(y + 4) + y = 20

Combine like terms:

2y + 4 = 20

Subtract 4 from both sides:

2y = 16

Divide both sides by 2:

y = 8

Now that we have the value of y, we can substitute it back into one of the original equations to find x:

x = y + 4
x = 8 + 4
x = 12

So, Doreen ran 12 miles and Ludy ran 8 miles.