SOLUTION: hi i need help with this problem. Together, Lateesha and John cna write a particular type of computer program in 15 hours. Alone, Lateesha can do the job 3 hours faster than Joh

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Question 136547This question is from textbook trigonometry
: hi i need help with this problem.
Together, Lateesha and John cna write a particular type of computer program in 15 hours. Alone, Lateesha can do the job 3 hours faster than John. Find the time that each person takes to write the computer program.
thank you very much for your time. This question is from textbook trigonometry

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes John to do the job
Then John works at the rate of 1/x of the job per hour
x-3=amount of time it takes Lateesha to do the job (we are told)
And Lateesha works at the rate of 1/(x-3) of the job per hour
Together, they work at the rate 1/x + 1/(x-3) of the job per hour (multiply numerator and denominator of each term by x(x-3)/x(x-3)) and we get:
(x-3+x)/x(x-3)=(2x-3)/x(x-3)
We are told that, together, they can do the job in 15 hours which means that together, they work at the rate of 1/15 of the job per hour, so our equation to solve is:
(2x-3)/x(x-3)=1/15 cross multiply (or multiply each term by 15x(x-3))
15(2x-3)=x(x-3) simplify
30x-45=x^2-3x subtract 30x from and add 45 to both sides
30x-30x-45+45=x^2-30x-3x+45 collect like terms
x^2-33x+45=0 quadratic in standard form; solve using quadratic formula

x=1.425 hrs
By inspection, we can see that x=1.425 hrs is not a realistic answer (if it takes both of them together 15 hrs, then John cannot do the job in 1.425 hrs)
and
x=31.575 hrs-----------------------amount of time it takes John to do the job working alone
x-3=31.575-3=28.575 hrs-------------amount of time it takes Lateesha working alone

CK
1/31.575 + 1/28.575 = 1/15
0.03167 + 0.03499 = 0.06667
0.06666-- ~~~~~0.06667

Hope this helps--ptaylor