Alice can build one section of a wooden fence with a base length of 18 meter and a height of 25 meter in 18 days. Bob can construct 80% of one side of a wooden deck with a length of ___ meter and a width of 25 meter in 28.8 days. There is a circular patio with a diameter of 28 meter. If Alice and Bob work together for 12 days on building the circular patio, then they would have finished constructing one side and built 59 square meters of the other side. (Note: The thickness of all the wooden structures is negligible).

What is the value that will come in place of the blank for the length of the wooden deck?

Solution

Area of one side of the triangular wall = (1/2) × base × height = (1/2) × 18 × 25 = 225 square meters So, painting efficiency of Alice = 225 ÷ 18 = 12.5 square meters/day Area of one side of the circular patio = π × radius² = (22/7) × (28/2) × (28/2) = 616 square meters So, total area painted by Bob and Alice = 616 + 59 = 675 square meters Out of which, area painted by Alice = 12 × 12.5 = 150 square meters So, area painted by Bob = 675 - 150 = 525 square meters So, painting efficiency of Bob = 525 ÷ 12 = 43.75 square meters/day So, area painted by Bob in 28.8 days = 43.75 × 28.8 = 1260 square meters = 80% of the area of one side of the wooden deck So, 100% of the area of one side of the wooden deck = 1260 ÷ 0.8 = 1575 square meters And so, length of the wooden deck = 1575 ÷ 25 = 63 meters