Question

Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 4 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?

Answer 1

The time taken for Company B to clear the parcel of land alone is 14.25 hours

Rate of work

• Time for Company B to clear the parcel of land alone = x
• Company B work rate = 1/x

• Time for Company A to clear the parcel of land alone = x + 4
• Company A work rate = 1/x+4

• Time for both Company to clear the parcel of land alone = 8 hours
• Both Company work rate = 1/8

1/8 = 1/x + 1/(x + 4)

1/8 = (x+4)+ (x) / (x)(x+4)

1/8 = (x+4+x) / (x² + 4x)

1/8 = 2x+4 / (x² + 4x)

cross product

1(x² + 4x) = 8(2x + 4)

x² + 4x = 16x + 32

x² + 4x - 16x - 32 = 0

x² - 12x - 32 = 0

Using quadratic formula

x = 14.25 or -2.25

The time taken for Company B to clear the parcel of land alone can only be positive,

Therefore, it is 14.25 hours

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