Fractions I guess?

Question

During a dig, an archaeological team starts at an elevation of −5 1/2 feet. At a rate of 2 3/4 feet per hour, the team digs deeper into the surface for 3 1/2 hours. For the next 4 1/2 hours, the team digs at a rate of 1 5/12 feet per hour. Then the team quits for the day.
How many feet did the archaeological team dig after 3 1/2 hours?
What was the team's elevation at the end of the day?

Answer 1

If they dig at a rate of 2 3/4 ft per hr for 3 1/2 hours, then the total distance dug after 3 1/2 hours is:

 

2 3/4 x 3 1/2 = 11/4 x 7/2 = 77/8 = 9 5/8 ft

 

If they then dig at a rate of 1 5/12 ft per hr for the next 4 1/2 hr, then that distance is:

 

1 5/12 x 4 1/2 = 17/12 x 9/2 = 153/24 = 6 9/24 ft

 

Therefore, at the end of the day, they have dug a total of 9 5/8 + 6 9/24 = 9 15/24 + 6 9/24 = 16 ft

 

Their elevation at the end of the day is -5 1/2 - 16 = -21 1/2 ft

Answer 2

a)  -5.5 - 2.75(3.5)

 

b) same as above, -4.5(0.0833333...)(5)     Note: 1/12 = 0.8333333...

 

or you can do the above calculations using rational numbers, if you choose.