1. It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.

2.2. A vine called the mile-a-minute weed is known for growing at a very fast rate. It can grow up to 0.5 ft per day. How fast in inches per hour can the mile-a-minute weed grow up to? Show your work using the correct conversion factors

Part 1:

We first convert all the time to hours and then sum them up.

There are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

There are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

Therefore, the number of hours it will take Mecury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours

Part 2:

Given that the vine grows at a rate of 0.5ft every day, this means that in 1 day, the vines grows by 0.5ft.

There are 12 inches in 1 foot, thus 0.5ft contains 12 x 0.5 = 6 inches.

i. e. the vine grows at a rate of 6 inches per day.

There are 24 hours in one day, so we have that the vine grows by 6 inches every 24 hours.

Given that the vine grows at a rate of 6 inches in 24 hours, the amount of growth of the vine every 1 hour is given by 6/24 = 0.25 inches.

Therefore, the mile-a-minute weed grows at a rate of 0.25 inches per hour.