James B. answered • 05/04/17

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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