Race the Sunset

At a glance

• Part 1: Alex finishes the first stage at 3:03 p.m.
• Part 2: The longest break that still finishes by sunset is 7 minutes. A 12-minute break makes Alex finish at 3:35 p.m., 5 minutes after sunset.

1. Find the first finishing time

Alex starts at 2:35 p.m. Add 28 minutes in two jumps: 25 minutes reaches 3:00 p.m., and 3 more minutes reaches 3:03 p.m.

2 :35 p.m. +28 minutes =3 :03 p.m.

She finishes the first building stage at 3:03 p.m.

2. Find the longest break and the planned finish

The final stage needs 20 minutes. Work backward from the 3:30 p.m. sunset:

3 :30 p.m. −20 minutes =3 :10 p.m.

Alex must start the final stage by 3:10. From 3:03 to 3:10 there are 7 minutes, so 7 minutes is the longest break that still finishes exactly at sunset.

With the planned 12-minute break, the final stage starts at

3 :03 p.m. +12 minutes =3 :15 p.m.

and ends at

3 :15 p.m. +20 minutes =3 :35 p.m.

That is 3 :35 −3 :30 =5 minutes late.

Why seven minutes is the maximum

A 7-minute break uses every available minute and finishes at 3:30. Any break longer than 7 minutes starts the final 20-minute stage after 3:10, so it must finish after sunset.

Check

The on-time schedule uses 28 +7 +20 =55 minutes. From 2:35 to 3:30 is exactly 55 minutes. The planned schedule uses 60 minutes, which explains the 5-minute overrun.