Answer:
1. Dave worked for 34 hours.
2. Perimeter of the rectangle is 172 cm.
Explanation:
1. Determination of the hours Dave worked.
Let D represent Dave.
Let M represent Mike.
Let J represent John.
Tota time worked by Dave, Mike and John is 56 hours. This can be written as:
D + M + J = 56 ..... (1)
Dave worked 6 more than 4 times as many hours as Mike. This can written as:
D = 6 + 4M .....(2)
John worked 6 less than 3 times as many hours as Mike. This can be written as:
J = 3M – 6 ........ (3)
Substituting the value of F and J into equation 1, we have:
D + M + J = 56
D = 6 + 4M
J = 3M – 6
6 + 4M + M + 3M – 6 = 56
6 – 6 + 4M + M + 3M = 56
8M = 56
Divide both side by 8
M = 56/8
M = 7
Substitute the value of M into equation (2) to obtain the value of D.
D = 6 + 4M
M = 7
D = 6 + 4(7)
D = 6 + 28
D = 34
Therefore, Dave worked for 34 hours .
2. Determination of the perimeter.
Length (L) = 64 cm
Width (W) = 22 cm
Perimeter (P) =?
P = 2(L + W)
P = 2 (64 + 22)
P = 2 (86)
P = 172 cm
Therefore, the perimeter of the rectangle is 172 cm