working at 75%efficiency the drying process takes four hours. how long does the drying process takes at 100%?

Answer 1

Assuming that there is a linear relationship between efficiency and time, this is a simple proportions problem.

(75/4) = (100/x) in other words, at 75% efficiency, it takes four hours, so at 100% efficiency, it will take x hours - solve for x.

x = 400/75

Answer 2

Since it was 75% efficient, 25% of the work was wasted, so the work should have taken 25% less time, or 3 hours total.

Another way to solve it:
- The rate was x liters/hour of liquid removed. If we have y liters removed at a rate of x liters/hour, it takes 4 hours.
y liters / x liters/hr = 4 hrs
- The new rate is (4/3)x liters/hour of liquid removed. If we divide the above equation by (4/3) on both sides, we get the following:
y liters / (4/3)x liters/hr = 4hrs/(4/3) = 4*(3/4) = 3hrs

If this doesn't make sense, then maybe try it with real numbers to understand it better. Suppose in a large drying operation, 75% rate is 75 liters/hr, and 100% is then 100 liters/hr. Then if it took 4 hrs at 75%, there were 4*75=300 total liters to remove. How long would it take to remove 300 liters at 100 liters/hr? answer 300/100 = 3 hrs

Robert S was going in the right direction in saying the 100% rate was 4/3 that of the 75% rate. His error, though, was in forgetting that since something is 4/3 as fast, it would require 1/(4/3) = 3/4 the time.

Answer 3

Presuming that the drying process is linear;-}
100% is 1/3rd faster than 75% efficiency.
Reducing 4 hours to minutes is 240 minutes.
Subtracting 1/3rd (80) leaves 160 minutes.
Coverting back to hours is 2 hours 40 minutes.