Machine X, working alone at a constant rate, can complete a manufacturing order in 4 hours… — GMAT

Machine X, working alone at a constant rate, can complete a manufacturing order in $4$ hours. Machine Y, working alone at a constant rate, can complete the same manufacturing order in $6$ hours. If Machine X and Machine Y work simultaneously at their respective constant rates, how many hours will it take them to complete $\frac{5}{6}$ of the manufacturing order?

$2$ hoursCevap
B
$2.4$ hours
C
$4.17$ hours
D
$5$ hours
E
$8.33$ hours

Cevap

2

hours

Machine X completes

\frac{1}{4}

of the order per hour and Machine Y completes

\frac{1}{6}

of the order per hour. Working together, their combined rate is

\frac{1}{4} + \frac{1}{6} = \frac{5}{12}

of the order per hour. To determine the time required to finish

\frac{5}{6}

of the order, divide the targeted work amount by the combined rate:

\frac{5/6}{5/12} = 2

hours.

Adım Adım Çözüm

Determine the individual work rates for Machine X and Machine Y

Rate of Machine X =

\frac{1}{4}

order per hour; Rate of Machine Y =

\frac{1}{6}

order per hour.

Work rate is defined as

\text{Rate} = \frac{\text{Work}}{\text{Time}}

Calculate the combined work rate when both machines work together

Combined Rate =

\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}

order per hour.

When machines work simultaneously, their individual rates add up.

Calculate the time required to complete

\frac{5}{6}

of the order using the combined rate

\text{Time} = \frac{\text{Work}}{\text{Combined Rate}} = \frac{5/6}{5/12} = \frac{5}{6} \times \frac{12}{5} = 2

hours.

Rearranging

\text{Work} = \text{Rate} \times \text{Time}

gives

\text{Time} = \frac{\text{Work}}{\text{Rate}}

Anahtar Kavram

Combined Work Rates

Tahmini Süre:2m 0s

Soru

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