Elizabeth took 13 minutes less than twice as long as Heather to solve the puzzle if their total time together was 23 minutes who took less time to solve the puzzle? How much less?

Liz spent 5 minutes, Heather spent 18, your total is 23 minutes.

Elizabeth took 13 minutes less to solve it.

can you explain better

To solve this problem, we need to set up equations based on the given information.

Let's assume that Heather took x minutes to solve the puzzle. According to the problem, Elizabeth took 13 minutes less than twice as long as Heather, which means she took (2x - 13) minutes to solve the puzzle.

The total time it took both of them together is 23 minutes. So, we can set up the equation:
x + (2x - 13) = 23

Simplifying the equation:
3x - 13 = 23
3x = 36
x = 12

Therefore, Heather took 12 minutes to solve the puzzle, and Elizabeth took 13 minutes less than twice that which is 2(12) - 13 = 11 minutes.

Comparing the times, we can see that Heather took longer by 1 minute. So, Heather took 1 minute more than Elizabeth to solve the puzzle.

E = 2H - 13

E + H = 23

Substitute 2H-13 for E in the second equation and solve for H. Put that value in the first equation and solve for E. Subtract H from E.