Tyra mows lawns at a constant rate. She can mow 3 lawns in 2 hours.

To answer the question about how much less time it would take Tyra and Ming working together to mow 3 lawns compared to Tyra working alone, we first need to calculate Tyra's individual mowing rate and then compare it with their combined rate.

Tyra's Rate: Tyra can mow 3 lawns in 2 hours. Therefore, her rate is: [ R_T = \frac{3 \text{ lawns}}{2 \text{ hours}} = 1.5 \text{ lawns per hour} ]

Time for Tyra to mow 3 lawns alone: Since Tyra’s rate is 1.5 lawns per hour, the time (( T_T )) it takes for her to mow 3 lawns alone is: [ T_T = \frac{3 \text{ lawns}}{1.5 \text{ lawns per hour}} = 2 \text{ hours} ]

Let's analyze the provided statements to determine the combined rate of Tyra and Ming:

Statement (1): Both Tyra and Ming mow lawns at the same rate.

If Ming also mows at the same rate as Tyra, ( R_M = R_T = 1.5 \text{ lawns per hour} ).
Combined rate (( R_{T+M} )) = ( R_T + R_M = 1.5 + 1.5 = 3 \text{ lawns per hour} ).
Time for Tyra and Ming to mow 3 lawns together:

( T_{T+M} = \frac{3 \text{ lawns}}{3 \text{ lawns per hour}} = 1 \text{ hour} ).
Statement (2): It takes Tyra twice as long to mow a lawn as it takes Tyra and Ming working together to mow a lawn.

This implies that Tyra and Ming together mow twice as fast as Tyra alone. If Tyra's time to mow one lawn is ( \frac{2}{3} ) hours (since she mows 1.5 lawns per hour), then Tyra and Ming together take ( \frac{1}{3} ) hour to mow one lawn.
The rate for Tyra and Ming together based on one lawn per ( \frac{1}{3} ) hour is ( 3 \text{ lawns per hour} ) (consistent with the calculation from statement (1)).
Time saved:

With Tyra alone, it takes 2 hours to mow 3 lawns.
With Tyra and Ming together, it takes 1 hour to mow 3 lawns.
Time saved = ( 2 \text{ hours} - 1 \text{ hour} = 1 \text{ hour} ).
Conclusion: Using either statement, we find that working together, Tyra and Ming can mow 3 lawns in 1 hour, which is 1 hour less than the time it takes Tyra alone. Thus, the answer to the question, using either statement, is that it would take Tyra and Ming 1 hour less to mow 3 lawns than Tyra alone.