SOLUTION: Help needed! Steve and Paula sell pies. It takes Paula one hour longer than Steve to take a day's supply of pies. Working together, it takes them 6/5 hours to bake the pies. How l

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Help needed! Steve and Paula sell pies. It takes Paula one hour longer than Steve to take a day's supply of pies. Working together, it takes them 6/5 hours to bake the pies. How l      Log On


   

Question 202019: Help needed!
Steve and Paula sell pies. It takes Paula one hour longer than Steve to take a day's supply of pies. Working together, it takes them 6/5 hours to bake the pies. How long would it take Steve working alone?
I solved by this way but when I check that's not correct! :
1%2F%281%2Bt%29%2B1%2Ft=1%2F%286%2F5%29
%282t%2B1%29%2Ft%5E2%2B1=5%2F6
6%282t%2B1%29=5%28t%5E2-1%29
5t%5E2-12t-11=0 and roots were 0.1 and -9.1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You have the correct equation, but made a mistake somewhere in the second step....



1%2F%281%2Bt%29%2B1%2Ft=1%2F%286%2F5%29 Start with the given equation.


1%2F%281%2Bt%29%2B1%2Ft=5%2F6 Rewrite 1%2F%286%2F5%29 as 5%2F6


Multiply EVERY term by the LCD 6t%281%2Bt%29 to clear out the fractions (to make things simpler).


6t%2B6%281%2Bt%29=5t%281%2Bt%29 Simplify


6t%2B6%2B6t=5t%2B5t%5E2 Distribute


6t%2B6%2B6t-5t-5t%5E2=0 Get all terms to the left side


-5t%5E2%2B7t%2B6=0 Combine like terms.


Notice that the quadratic -5t%5E2%2B7t%2B6 is in the form of At%5E2%2BBt%2BC where A=-5, B=7, and C=6


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%28-5%29%286%29+%29%29%2F%282%28-5%29%29 Plug in A=-5, B=7, and C=6


t+=+%28-7+%2B-+sqrt%28+49-4%28-5%29%286%29+%29%29%2F%282%28-5%29%29 Square 7 to get 49.


t+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%28-5%29%29 Multiply 4%28-5%29%286%29 to get -120


t+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%28-5%29%29 Rewrite sqrt%2849--120%29 as sqrt%2849%2B120%29


t+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%28-5%29%29 Add 49 to 120 to get 169


t+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%28-10%29 Multiply 2 and -5 to get -10.


t+=+%28-7+%2B-+13%29%2F%28-10%29 Take the square root of 169 to get 13.


t+=+%28-7+%2B+13%29%2F%28-10%29 or t+=+%28-7+-+13%29%2F%28-10%29 Break up the expression.


t+=+%286%29%2F%28-10%29 or t+=++%28-20%29%2F%28-10%29 Combine like terms.


t+=+-3%2F5 or t+=+2 Simplify.


So the possible solutions are t+=+-3%2F5 or t+=+2


However, a negative time value doesn't make much sense. So we can ignore t+=+-3%2F5


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Answer:

So the solution is t+=+2 which means that it takes Steve 2 hours if he were working alone.