I got 18 min. Why was that wrong?

Question

Julie=8 min mile/ Anna=12 min mile. Began at same place on mile track. Both ran for 30 mins. How many min. passed before they were at the starting point together

Answer 1

Julie                    Anna

8 min, 1 mile       12 min, 1 mile

16 min, 2 miles    24 min, 2 miles

24 min, 3 miles    36 min, 3 miles

in 24 minutes they are at the starting point together again

24 is the LCM of 8 and 12

in 18 min, Julie ran 18/8=2.25 miles and Anna ran 18/12=1.5 miles

Answer 2

Here you are looking for the least common multiple of their mile times as that will put them both at the starting point of a one mile track. You can do this quickly through some trial and error:

 

12 is not divisible by 8

 

12 x 2 = 24 which is divisible by 8

 

After 24 minutes they will both be at the starting point again, Anna will have ran 24/12 = 2 miles and Julie will have ran 24/8 = 3 miles.