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JAMB 1984 · UME · Q21

Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in xx days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by xx?

Worked solution (try it first)
  1. In one day Tunde does 1x\frac1x of the work and Shola does 1x+15\frac{1}{x + 15}.
  2. Together they do 118\frac{1}{18}.
  3. So 1x+1x+15=118\dfrac1x + \dfrac{1}{x + 15} = \dfrac{1}{18}.
  4. Multiply through by 18x(x+15)18x(x + 15): 18(x+15)+18x=x(x+15)18(x + 15) + 18x = x(x + 15).
  5. Expand: 36x+270=x2+15x36x + 270 = x^2 + 15x.
  6. Bring everything to one side: x2−21x−270=0x^2 - 21x - 270 = 0, option C.

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