Drill Sergeant Jones can scare one new recruit every 16 seconds. Drill Sergeant Smith can scare one every 22 seconds. Together, how many seconds will it take -

Question

to scare 38 new recruit? Please help me!!

Answer 1

 

Rate Time = Distance

 

Jones' rate   => 1 recruit every 16 seconds ... or (1/16) of a recruit, per second

Smith's rate => 1 recruit every 22 seconds ... or (1/22) of a recruit, per second

 

The combined rate => (1/16 + 1/22) recruits, per second

 

       1/16 + 1/22

 

    The LCM of 16 and 22 is 176, so rewrite both fractions such that 176 is the common denominator

 

       (1/16)(11/11) + (1/22)(8/8)

       (11/176) + (8/176)

       (19/176)

 

    The combined rate of scaring recruits is 19/176 recruits per second

 

     Set up a proportion ... let x = number of seconds we are looking for

 

     (19/176) recruits               38 recruits

    ------------------------  =  --------------------------

        1  sec                               x seconds

 

    Cross multiply

 

(19/176)x = 1(38)

             x = 38(176/19)

             x = 352 seconds

 

CHECK:  in 352 seconds, since Jone's rate is 1 recruit every 16 seconds, she will scare 352/16, or 22 recruits

             in 352 seconds, since Smith's rate is 1 recruit every 22 seconds, she will scare 352/22, or 16 recruits

             22 + 16 = 38 ... the combined number of recruits scared in 352 seconds