Lisa​ can fill a certain order in 8 hours. Felipe​ needs 11 hours to do the same job. Working​ together, how long will it take them to fill the​ order?

Question

Lisa can fill a certain order in 8 hours. Felipe needs 11 hours to do the same job. Working together, how long will it take them to fill the order?

Answer 1

Lisa can fill a certain order in 8 hours ... Lisa does 1/8 of the order per hour

 

Felipe needs 11 hours ...  Felipe does 1/11 of the order per hour

 

Together they do:  1/8 + 1/11 = 11/88 + 8/88 = 19/88 of the order per hour

 

Multiply that total per hour by x hours and set equal to one...

    one represents the entire order or 100%

 

(19/88)x = 1

x = 88/19

x = 4 12/19 hours

 

If we need hours and minutes:

(12/19 hours)(60 mins/hr) = 37.895 minutes

 

Note:  0.895 minutes is 53.7 seconds

 

Total time:  4 hours 37 minutes 53.7 seconds

 

 

Answer 2

Develop this equation - To find the time for both working together, put the individual times in the denominators:

 

1/8 + 1/11 = 1/x

 

 

Solve for x:

 

Get a common denominator:

 

11/88 + 8/88 = 1/x

 

19/xx = 1/x

 

Cross multiply:

 

19x = 88

 

 

x = 4.63 hours