Question 265496
rate * time = units


this translates to:


number of units produced per minute * number of minutes = number of units produced.


the number of units produced is 1 full pool.


jim can fill the pool in 30 minutes which means jim can fill 1/30 of the pool each minute.


1/30 * 30 = 1


sue can fill the pool in 45 minutes which means sue can fill 1/45 of the pool each minute.


1/45 * 45 = 1


tony can fill the pool in 1 and 1/2 hours which means that tony can fill the pool in 90 minutes which means that tony can fill 1/90 of the pool each minute.


1/90 * 90 = 1


when they work together, their combined rates are additive.


if we let x = the number of minutes it takes to fill the pool, then we have:


rate * x = 1


the combined rate is equal to jim's rate plus sue's rate plus tony's rate.


formula becomes:


(1/30 + 1/45 + 1/90) * x = 1


1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 = 1/15.


their combined rate is 1/15 of the pool every minute.


formula becomes:


1/15 * x = 1


multiply both sides of this equation by 15 to get:


x = 15


working together, they will take 15 minutes to fill the pool.


in 15 minutes jim has filled 1/30 * 15 = 15/30 = 1/2 of the pool.


in the same 15 minutes, sue has filled 1/45 * 15 = 1/3 of the pool.


in the same 15 minutes, tony has filled 1/90 * 15 = 1/6 of the pool.


1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1 full pool.


your answer is selection B (15 minutes).