Answer:
9 days
Explanation:
Ordinarily, a rate that involves time will have the time unit in the denominator. Here, we have time as the dependent variable, so we want the time unit in the numerator for this problem. Then the "unit rate" is ...
days/liter = (5 days)/(10 liters) = (1/2) day/liter
Then for 18 liters, we multiply by the unit rate to get days:
(18 liters)(1/2 day/liter) = 9 days
It will take Matthew 9 days to jar 18 liters if he maintains his rate.
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The other way to write this unit rate is ...
1/(1/2 day/liter) = 2 liters/day
Then to find days, we'd have to divide the desired volume by this rate:
(18 liters)/(2 liters/day) = 9 days