Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?
A
x2 - 5x - 10 = 0
B
x2 - 20x + 360 = 0
C
x2 - 21x - 270 = 0
D
3x2 - 65x + 362 = 0
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Tunde and Shola can do the work in 18 days.
Both will do the work in \(\frac{1}{18}\) days.
But Tunde can do the whole work in x days; Hence he does \(\frac{1}{x}\) of the work in 1 day.
Shola does the work in (x + 15) days; hence, he does \(\frac{1}{x + 15}\) of the work in 1 day.
\(\frac{1}{x} + \frac{1}{x + 15} = \frac{1}{18}\)
\(\frac{2x + 15}{x^{2} + 15x} = \frac{1}{18}\)
\(x^{2} + 15x = 36x + 270\)
\(x^{2} + 15x - 36x - 270 = 0\)
\(x^{2} - 21x - 270 = 0\)
Source: Myschool Past Questions Archive (Record #32421)