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Mixture problem - my bad or a typo?

Expert replies
by iwhite » Thu May 06, 2010 4:20 pm
I'm working on one of the PS problem:
A certain tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride. The proportion of sodium chloride in the tank is 40% by volume and the capacity of the tank is 24 gallons. If the water evaporates from the tank at the rate of 0.5 gallons per hour, and the amount of sodium chloride stays the same, what will be the concentration of water in the mixture in 2 hours?
The solution reads like:
First, let's find the initial amount of water in the tank:
Total mixture in the tank =1/4 × (capacity of the tank) = (1/4) × 24 = 6 gallons
Concentration of water in the mixture = 100% - (concentration of sodium chloride) = 100% - 40% = 60%
Initial amount of water in the tank = 60% × (total mixture)= 0.6 × 6 = 3.6 gallons

Next, let's find the amount and concentration of water after 2 hours:
Amount of water that will evaporate in 2 hours = (rate of evaporation)(time) = 0.5(2) = 1 gallon
Remaining amount of water = initial amount - evaporated water = 3.6 - 1 = 2.6 gallons
Remaining amount of mixture = initial amount - evaporated water = 6 - 1 = 5 gallons
...
Please, take a look at line in bold. Shouldn't the initial amount be 6-3.6 = 2.4 ? Thank you.
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Source: — Problem Solving |

by kstv » Thu May 06, 2010 4:55 pm
2.4 is the volume of sodium Chloride which remains constant. From 6 gallons of water + NaCl only 1 gallon of water has evaporated. In the remaining 5 gallons there is 2.6 & 2.4 gallons of water and NaCl respectively.
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