Lisa​, an experienced shipping​ clerk, can fill a certain order in 14 hours. Tom​, a new​ clerk, needs 17 hours to do the same job. Working​ together, how long will it take them to fill the​ order?

Answer 1

To find out how long it takes for Lisa and Tom to fill the order together, we can use the concept of work rates.

1. Calculate the work rates:

   • Lisa's work rate: \( \frac{1 \text{ order}}{14 \text{ hours}} = \frac{1}{14} \text{ orders per hour} \)
   • Tom's work rate: \( \frac{1 \text{ order}}{17 \text{ hours}} = \frac{1}{17} \text{ orders per hour} \)

2. Combine their work rates: To find their combined work rate, we add the two work rates together: \[ \text{Combined work rate} = \frac{1}{14} + \frac{1}{17} \]

   To add these fractions, we need a common denominator. The least common multiple (LCM) of 14 and 17 is 238.

   Converting the fractions: \[ \frac{1}{14} = \frac{17}{238} \] \[ \frac{1}{17} = \frac{14}{238} \]

   Now, add the two: \[ \text{Combined work rate} = \frac{17}{238} + \frac{14}{238} = \frac{31}{238} \text{ orders per hour} \]

3. Calculate the time taken to complete 1 order together: To find how long it takes for them to complete one order together, we take the reciprocal of their combined work rate: \[ \text{Time} = \frac{1 \text{ order}}{\frac{31}{238} \text{ orders per hour}} = \frac{238}{31} \text{ hours} \]

   Calculating the division: \[ \frac{238}{31} = 7.677 \text{ hours} \approx 7 \text{ hours and } 41 \text{ minutes} \]

So, working together, Lisa and Tom can fill the order in approximately 7 hours and 41 minutes.