Question 16595: please help me solve the math problem i have . I would be glad if you can send me the answers with explaination so i can study how it is solved. Thanks !
question # 1
Working together, two details of airforce reservists can load a C-130 aircraft with relief supplies for hurricane victims in 6 hours . Working alone, the first detail can load the plane in two hours less time than the second detail can when working alone. How long would it take for the second detail, working alone , to load the plane ? ( neglect t value that would make details time negative).
question # 2
At a juice processing plant , one pipe can fill a storage tank with cranberry juice in two hours. Another pipe can fill the same tank with apple juice in 3 hours. If both pipes are open, how long does it take to fill the tank cran-apple juice ?
question # 3
Twice a number plus 1 is divided 1 less than half the number. The result is 5. What is the number ?
My pleasure if these problems are answered with solution. Glad i have found this website.
respectfully yours
suanie
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Question #1.
If details 1 and 2 (D1 + D2) together can load the plane in 6 hours, then they can load 1/6 of the plane in 1 hour.
But, since D2 takes 2 hours longer to load than D1, then in 1 hour, working together, their loading rates would be:
 where t is the loading time in hours, and this is equal to 1/6.
So we have:
 Simplify and solve for t, the loading time in hours.
 Multiply both sides by 
 Multiply both sides by 6.
 Put this into standard quadratic form.
 Solve for t using the quadratic formula: 
 or  Discard the negative result.
t = 11.1 hours This is the time taken by detail 1 to load the C-130
t+2 = 13.1 hours This is the time taken by detail 2 to load the C-130.
Check:
In 1 hour, detail 1 can load 1/11 of the plane.
In 1 hour, detail 2 can load 1/13 of the plane.
Together, they can load 1/11 + 1/13 = 24/143 of the plane.
It will take them 143/24 hours to load the plane together
143/24 hours= 5.958 hours This is approximately 6 hours. It's not exactly 6 because we had to take the square root of 37 resulting in an irrational number.
Problem #2.
If it takes the cranberry juice pipe 2 hours to fill the tank, then it can fill 1/2 ths tank in 1 hour.
If it takes the apple juice pipe 3 hours to fill the tank, then it can fill 1/3 of the tank in 1 hour.
So, together,the pipes can fill (1/2 + 1/3 = 5/6) of the tank in 1 hour.
Therefore, it would take them 6/5 hours to completely fill the tank working together.
6/5 hours = 1 hour and 12 minutes.
Problem #3.
Let n be the number.
 Simplify.
 Multiply both sides by (n-2)
 Subtract 4n from both sides.
 Add 10 to both sides.
The number is 12.
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