Final answer:
To find when the green and yellow watches were last synchronized, one must calculate the time difference caused by their inaccuracies. The green watch runs 1 minute fast and the yellow 2 minutes slow per hour. By calculating the accumulated difference, we determine they were last set together at 11:20 A.M. on Tuesday.
Step-by-step explanation:
The question concerns determining the last time two watches, which run at different inaccuracies, were set together. One watch runs 1 minute fast each hour, and the other runs 2 minutes slow each hour. As of Wednesday morning, there is a 1-hour difference between the green and yellow watches, with the green watch displaying 7:20 A.M. and the yellow displaying 6:20 A.M. To find out when they were last synchronized, we have to account for the differences in time caused by their inaccuracies.
To solve this, we can set up an equation that accounts for the rate at which each watch loses or gains time. Since the two watches currently show a one-hour difference, we need to find a time that justifies this difference based on their respective rates of losing and gaining time. The difference in their times accumulates at a rate of 3 minutes per hour (1 minute fast + 2 minutes slow). After calculating the number of hours that have passed to generate a 60-minute difference at a 3-minute discrepancy per hour, we find that they were last set together 20 hours ago.
Therefore, if the green watch reads 7:20 A.M. on Wednesday, counting 20 hours back, we arrive at the last synchronization time. Subtraction of 20 hours from 7:20 A.M. Wednesday results in 11:20 A.M. Tuesday. That is the correct time on Tuesday when the watches were last set together.