Explanation Given: Two people can mow a lawn in four hours. One person can do this job alone in one hour faster than another person. Formula used: Shreedhracharaya formula x = − b ± b 2 − 4 a c 2 ( a ) . Calculation: Let the time required by the faster person to mow the lawn be x hours. Therefore, the time required by the slower person to mow the lawn is ( x + 1 ) hours. According to the provided condition, 4 x + 4 x + 1 = 1 4 ( x + 1 ) + 4 x x ( x + 1 ) = 1 4 x + 4 + 4 x x 2 + x = 1 8 x + 4 x 2 + x = 1 Multiply both sides by x 2 + x , 8 x + 4 x 2 + x ( x 2 + x ) = 1 ( x 2 + x ) 8 x + 4 = x 2 + x Subtract 8 x + 4 from both side, 8 x + 4 − 8 x − 4 = x 2 + x − 8 x − 4 x 2 − 7 x − 4 = 0 Compare x 2 − 7 x − 4 = 0 with the standard quadratic equation a x 2 + b x + c = 0 will provide, a = 1 , b = − 7 and c = − 4

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ISBN: 9780136553632

Author: Blitzer

Publisher: VST

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Chapter 8.2, Problem 87ES

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To calculate: The time required by each person working alone to mow the lawn.

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Chapter 8.2, Problem 86ES

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The time required by each person working alone to mow the lawn.

Solution Summary: The author calculates the time required by each person working alone to mow the lawn, based on the Shreedhracharaya formula.

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