Ten minutes before putting the cake in the oven, I put my cat outside. The cake should cook for 35 minutes, so I set the alarm to go off 35 minutes after putting the cake in the oven. Immediately after, I made a coffee for myself, which took me 6 minutes. Three minutes before finishing my coffee, my cat came back inside. This was 5 minutes before the alarm went off. The phone rang halfway between when I finished making the coffee and when the cat came back inside. I talked on the phone for 5 minutes and then hung up. It was then 3:59 PM.
(a) What time did I put my cat outside?

(b) How many minutes after putting the cat outside did the alarm go off?

(c) How long had the cat been outside when the phone rang?
Let's list the events that occurred and count the time spent on each. The first activity was putting the cat outside the house, so our list starts with this activity, and the time is counted from it.

| Activity | Time after the cat was put outside the house |
| :---: | :---: |
| Cat outside the house | 0 minutes |
| Cake in the oven | 10 minutes |
| Make coffee | $10+6=16$ minutes |
| Alarm clock rings | $35+10=45$ minutes |
| Cat enters the house | $45-5=40$ minutes |
| Finish drinking coffee | $40+3=43$ minutes |
| Phone rings | $16+(40-16) \div 2=28$ minutes |
| Hang up the phone | $28+5=33$ minutes |

Now, we can provide the answers.

(a) At 3:59, I hung up the phone, which occurred 33 minutes after putting the cat outside the house. Since $59-33=26$, I put the cat outside at $3 \mathrm{~h} 26 \mathrm{~min}$.

(b) The alarm clock rings 45 minutes after putting the cat outside the house.

(c) The cat had been outside for 28 minutes when the phone rang.

We can determine the exact time each activity occurred, as shown in the following table.

| Activity | Time after the cat was put outside the house | Time |
| :---: | :---: | :---: |
| Cat outside the house | $0 \mathrm{~min}$ | $59-33=3 \mathrm{~h} 26 \mathrm{~min}$ |
| Cake in the oven | $10 \mathrm{~min}$ | $26+10=3 \mathrm{~h} 36 \mathrm{~min}$ |
| Make coffee | $10+6=16 \mathrm{~min}$ | $26+16=3 \mathrm{~h} 42 \mathrm{~min}$ |
| Alarm clock rings | $35+10=45 \mathrm{~min}$ | $26+45=4 \mathrm{~h} 11 \mathrm{~min}$ |
| Cat enters the house | $45-5=40 \mathrm{~min}$ | $26+40=4 \mathrm{~h} 06 \mathrm{~min}$ |
| Finish drinking coffee | $40+3=43 \mathrm{~min}$ | $26+43=4 \mathrm{~h} 09 \mathrm{~min}$ |
| Phone rings | $16+(40-16) \div 2=28 \mathrm{~min}$ | $26+28=3 \mathrm{~h} 54 \mathrm{~min}$ |
| Hang up the phone | $28+5=33 \mathrm{~min}$ | $26+33=3 \mathrm{~h} 59 \mathrm{~min}$ |