SS1 Math cooperation skills

2010-05-03 12:13 am

Andy requires 1(2/3) hours more than Lawrence to lay tiles on a floor.
When they work together, they can finish the job in 2 hours. How long does
Andy require to lay the tiles alone?

Ans: 5 hours

回答 (1)

用戶2053

2010-05-03 12:29 am

✔ 最佳答案

Let x hours be the times of Andy require to lay the tiles alone , then
Lawrence require x - (1+2/3) = x - 5/3 hours to lay the tiles alone,
Andy can finish 1/x of the total job per hours while
Lawrence can finishe 1/(x - 5/3) .
2 hours they can finish all :
2( 1/x + 1/(x - 5/3) ) = 1
2[(x - 5/3) + x] = x(x - 5/3)
4x - 10/3 = x^2 - (5/3)x
12x - 10 = 3x^2 - 5x
3x^2 - 17x + 10 = 0
(3x - 2)(x - 5) = 0
x = 2/3(rejected since 2/3 < 2 hours is impossible) or x = 5
Andy require 5 hours to lay the tiles alone.

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