Question 1189837: Four friends decide to meet at 6 pm. They each set their watches to what they think is the correct time, using a clock at home. Unfortunately, all of their clocks show the wrong time. Alice thinks her clock at home is 8 minutes fast when it is really 3 minutes slow; Barney thinks his clock is 9 minutes slow when it is actually 6 minutes fast; Clive thinks his is 3 minutes fast but it's really 4 minutes slow; Dolores thinks hers is 3 minutes slow when it's actually 22 minutes fast; Elisha thinks her clock at home is 7 minutes fast when it is really 7 minutes slow. If they all arrive at the restaurant at 6 pm on their incorrectly set watches, the person who arrives the latest is
A) Alice B) Barney C) Clive D) Dolores E) Elisha
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52752)   (Show Source):
Answer by math_tutor2020(3816)  (Show Source):
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Given info:
| Person | They think their clock is... | Their clock is actually... | | Alice | 8 minutes fast | 3 minutes slow | | Barney | 9 minutes slow | 6 minutes fast | | Clive | 3 minutes fast | 4 minutes slow | | Dolores | 3 minutes slow | 22 minutes fast | | Elisha | 7 minutes fast | 7 minutes slow |
Let's say hypothetically that when each person is setting their watch, the official time is 3:00 PM.
Now let's consider Alice. Her clock is actually 3 minutes slow. Her clock displays 2:57 PM (which is 3 minutes shy of 3:00 PM). Alice thinks her clock is 8 minutes fast.
To counterbalance things, she'll subtract 8 minutes from the clock's display to get 2:49 PM.
Alice sets her watch to 2:49 PM when the true time is 3:00 PM.
Notice the gap from 2:49 (what Alice thinks the time should be) and 3:00 (what the time is officially) is exactly 11 minutes.
Furthermore, notice that 3+8 = 11.
In other words, Alice clock is 3 min slow and she mistakenly slows it down another 8 min to have it be 11 min slow overall.
Barney has his clock 6 minutes fast and he thinks its 9 minutes slow. Therefore, he'll add 9 to the time on his clock to be 6+9 = 15 minutes fast.
The other clocks are adjusted in a similar fashion
After such adjustments, we have this
| Person | His or her watch is... | | Alice | 11 minutes slow | | Barney | 15 minutes fast | | Clive | 7 minutes slow | | Dolores | 25 minutes fast | | Elisha | 14 minutes slow |
The person with the slowest watch will arrive at the restaurant last. That table shows that Elisha is the unfortunate one to draw the shortest straw here.
If you're curious about each person's arrival time (the true time, not what their watch says), then we would have this
| Person | When they *actually* arrive at the restaurant | Notes | | Alice | 6:11 PM | 11 minutes after the true time of 6:00 PM | | Barney | 5:45 PM | 15 minutes before the true time of 6:00 PM | | Clive | 6:07 PM | 7 minutes after the true time of 6:00 PM | | Dolores | 5:35 PM | 25 minutes before the true time of 6:00 PM | | Elisha | 6:14 PM | 14 minutes after the true time of 6:00 PM |
This table helps further show that Elisha is the last to arrive.
Answer: E) Elisha
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