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1.If Samantha and Logan can do their paper route together in 45 minutes, how many hours would it take each of    the to do it alone, given Samantha is three times as fast as Logan?
                             Rate        Time    Work Done
|Samantha           |             |          |                  |
| Logan                |             |          |                  |
 2. To keep his baseball team hydrated, Daniel mixes powdered sports drink with cold water. For best taste mix should be 96% water. If Daniel has used 16 scoops of powder and 2 quarts of water, how many gallons of water should he add, given each scoop is 1/4cup

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Bill P. | A math tutor that is both knowledgeable and patient in secondary math.A math tutor that is both knowledgeable ...
For the baseball team's sports drink, one must use 6 gallons of water with 16 scoops of powder to yield a mixture that is 96% water (and 4% powder). Since initially there was 2 quarts of water, or 1/2 gallon of water, Daniel needs to add 5.5 extra gallons of water. The yield will be 100 cups (800 ounces) of sports drink.
Calculations: 16 scoops times 1/4 cup each = 4 cups of powder Since this is supposed to be 96% water, we need the powder to be only 4% of the total. If 4 cups is 4%, of the total, then 100 cups must be 100% of the total. So, we need 96 cups (or 96 * 8 = 768 ounces of water. Initially 64 ounces (2 quarts) of water were mixed with the 4 cups of powder. We need to add 768 - 64 or 704 ounces of water to complete the task. 704 ounces is 5.5 gallons since 1 gallon is 128 ounces.
Daniel needs to add 5 and one-half gallons of water to his mixture. The result will be 6.25 gallons of sports drink. Hopefully, that will be sufficient to keep his team hydrated. If the game goes extra innings (like the game between the San Francisco Giants and Washington Nationals on Saturday, October 4th, 2014, which lasted 18 innings) they may need to make some more.
Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.
Let x be the amount of hours spent by Samantha when she works alone, and 3x - time spent by Logan.
First, You have to find how much work can be done each of these girls per unit of time. For Samantha it is 1/x, for Logan - 1/3x. Because 45 minutes is 3/4 of an hour, together they could have done 4/3 part of the work per hour. thus we have the equation:
                   1/x    + 1/3x    = 4/3
Which means x = 1 and 3x = 3. Thus, Samantha can do the work in one hour while Logan does it in 3 hours.
Carol H. | Experienced Mathematics Tutor w/ Master's Degree in MathExperienced Mathematics Tutor w/ Master'...
4.9 4.9 (276 lesson ratings) (276)
Let x = the amount of minutes it would take Samantha to do the job alone
Let 3x = the amount of minutes it would take Logan to do the job alone  
 x 3x = 1  multiply both sides of the equation by 45
45    45
x + 3x = 45
      4x = 45
       4      4
        x = 11 1/4 minutes for Samantha
       3x = 3(11 1/4)
         x = 33 3/4 minutes for Logan


Your result shows that each of these girls works faster than when they work together.