OG - PS - #154

[mariela]

If 3/5 of the work is done in 8 hours, does that mean that I need to solve for the rate and plug that back in to get the time for the remaining 2/5 of the work? What is a quicker way to solve this problem.

[esledge]

Hi Mariela,

An alternative to solving for the rate (or to solving for the total time, as in the O.G. solution) would be to set up a comparison. Since the pool is filled at a constant rate, the rate of filling the first 3/5 of the pool is the same as the rate of filling the last 2/5 of the pool. Rate = Amount filled / Time, so:

Rate = (3/5 capacity) / 8 hours = (2/5 capacity) / x hours

Cross-multiply:
(3/5)(x) = (2/5)(8 hours)

Isolate x:
x = (2/5)(8 hours)(5/3)
x = (2/3)(8 hours)
x = 16/3 hours = 5 hours 20 minutes

Notice that this answer "makes sense." If the pool were 5 units in capacity, the amount filled so far is 3 units (3/5 of the capacity). There are 2 more units to go, which should take 2/3 as long as it did to fill the first 3 units. 2/3 of 8 hours is 5 hours 20 minutes.