Question 5: A company could use any of the 3 builder (Anthony, Bob and Charles) to build a wall. Anthony would take A days to build the wall. Likewise, Bob and Charles would take B days and C days to build the wall respectively.
Anthony and Bob take 16.8 days to complete a wall.
Anthony and Charles take 21 days to complete a wall.
Bob and Charles take 28 days to complete a wall.
Solution:
Anthony builds 1 wall in A days. Hence, Anthony builds 1/A wall in 1 day.
Similarly, Bob builds 1/B wall in 1 day, and Charles builds 1/C wall in 1 day.
In 1 day, Anthony and Bob together will build (1/A + 1/B) wall. In 16.8 days, Anthony and Bob will build [16.8x(1/A + 1/B)] wall which is 1 wall since Anthony and Bob complete the wall in 16.8 days. Hence, we get the following equations:
16.8(1/A + 1/B) = 1
21(1/A + 1/C) = 1
28(1/B + 1/C) = 1
Implying..
1/A + 1/B = 1/16.8 -------- (1)
1/A + 1/C = 1/21 ---------- (2)
1/B + 1/C = 1/28 ---------- (3)
(1)+(2)-(3)
2(1/A) = 1/16.8 + 1/21 - 1/28 = 1/14
Therefore, 1/A = 1/28, hence, A = 28.
From (1), 1/B = 1/16.8 - 1/28 = 1/42. Hence, B = 42.
From (2), 1/C = 1/21 - 1/28 = 1/84. Hence, C = 84.
Answer: A+B+C=154
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