# One watch is 1 minute slow at 1 pm on Tuesday and 2 minutes fast at 1 am on Friday. When did it show that correct time?

## (1) 5:00 am on Wednesday (2) 5:00 pm on Wednesday (3) 9:00 am on Wednesday (4) 9:00 pm on Wednesday

Aug 10, 2018

(3) 9:00am Wednesday

#### Explanation:

The correct time will be shown when the watch has gained 1 minute.
We are told that the watch gains 3 minutes between 1pm Tuesday and 1am Friday.

First let's convert the time duration to minutes.

1pm Tuesday to 1pm Thursday is 2 full days $= 2 \cdot 24$hr

1pm Thursday to 1am Friday is 12hr

Total time $= 48 + 12 = 60 h r = 60 \cdot 60 = 3600 \min$

So the watch gains $3 \min \text{per } 3600 \min$

But we only want 1 min gain for the watch time to be correct.

This will happen after $\frac{3600}{3} = 1200 \min$

Let's convert this back to hours and minutes so we can add it to the start time, to find the time that the watch shows the correct time.

$\frac{1200 \min}{60 \frac{\min}{h r}} = 20 h r$

1pm Tues + 20hr = (1pm Wed - 4hr) = 9am Wednesday