Answer:
9 linear feet of lumber will be needed.
Explanation:
Since the ramp is going to be 3 ft wide and 6 ft long and we have 6 in wide boards, we are going to be stacking the boards side by side to cover the length and width of the ramp.
Let n boards cover the width of the ramp, then number of boards × width of one board = width of ramp.
So, n × 6 in = 3 ft
Since 12 in = 1 ft, we have
n × 6 in = 3 ft = 3 × 1 ft = 3 × 12 in
n × 6 in = 36 in
n = 36 in/6 in
n = 6
Let n' boards cover the length of the ramp, then number of boards × width of one board = length of ramp.
So, n' × 6 in = 6 ft
Since 12 in = 1 ft, we have
n' × 6 in = 6 ft = 6 × 1 ft = 6 × 12 in
n' × 6 in = 72 in
n' = 72 in/6 in
n' = 12
Thus, the total number of boards needed is n" = n + n' = 6 + 12 = 18
So, the number of inches of board needed is thus n" × width of one board = 18 × 6 in = 108 in
Now, since 12 in = 1 ft, 1 in = 1/12 ft
108 in = 108 × 1/12 ft = 108/12 ft = 9 ft
So, 9 linear feet of lumber will be needed.