Rose and Helen can finish a cross-stitch project in 4 hours if they work together. If it would take Rose 6 hours more than Helen to finish the project alond, hiw long would each need ti finish the project alone, how long would each need to finish the project working alone?
Answers
Given :-
- Rose and Helen can finish a cross-stitch project in 4 hours if they work together.
- it would take Rose 6 hours more than Helen to finish the project alone.
To Find :-
- How long would each need to finish the project working alone ?
Solution :-
Let us assume that, helen can finish the Project alone in = x hours.
Than,
→ Rose can finish the project alone in = (x + 6) hours.
given that, both can finish the project in 4 hours.
So,
→ 1/x + 1/(x + 6) = 4
→ (x + 6 + x) /x(x + 6) = 4
→ 4(2x + 6) = x² + 6x
→ 8x + 24 = x² + 6x
→ x² + 6x - 8x - 24 = 0
→ x² - 2x - 24 = 0
→ x² - 6x + 4x - 24 = 0
→ x(x - 6) + 4(x - 6) = 0
→ (x - 6) + (x + 4) = 0
→ x = 6 and (-4).
since negative value of hours is not possible.
Therefore,
→ Helen can finish the Project alone in = x = 6 hours.
→ Rose can finish the project alone in = (x + 6) = (6 + 6) = 12 hours.
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