First, let x= initial mph and M= initial miles ran.

So its easy to see that

x mph * 1.5 hours = M miles

Now we are told that she has upped her speed by 3 mph

so now

(x+3)mph * 1.5 hours = 2M – 1.8 (remember she runs 1.8 miles less than twice the orig distance.)

Write both equations:

x*1.5 = M

(x+3)*1.5 = 2M-1.8

Distribute the second equation

1.5x + 4.5 = 2M – 1.8

Substitute the first equation into second (remember 1.5x=M)

M + 4.5 = 2M -1.8

Subtract M from both sides

4.5 = M – 1.8

Add 1.8 to both sides

6.3 = M

So her initial distance was 6.3 miles

Go back to the first equation

x*1.5 = M

x*1.5 = 6.3

x = 4.2 mph this was her initial speed.

Her new speed is 3 mph faster

4.2 + 3 = 7.2 mph

Her new distance is

1.5 * 7.2 = 10.8 miles

Take care!