SOLUTION: A takes 16 Days less than B to do a piece of work. If both working together can do it in 15 days ,in how many days will A alone complete the work. My solution: Let time taken b

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A takes 16 Days less than B to do a piece of work. If both working together can do it in 15 days ,in how many days will A alone complete the work. My solution: Let time taken b      Log On


   

Question 1085310: A takes 16 Days less than B to do a piece of work. If both working together can do it in 15 days ,in how many days will A alone complete the work.
My solution:
Let time taken by B be x
Time taken by A= x-16
One day work of B =1/x
One day work of A =1/x-16
They together complete the work in 15 days
A+B one day work = 1/15
According to question
1/(x-16) -1/x =1/15
X-(x-16)/x^2-16x= 1/15
16/x^2-16x= 1/15
15×16=x^2-16x
x^2-16x-240=0
On solving this eq my ans is not coming. Please give me the correct solution.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
"a piece of work", 1 job.

A takes 16 days less than B...
             RATES
A            1/(x-16)

B            1/x

Together     1%2F%28x-16%29%2B1%2Fx=1%2F15

15x%28x-16%29%281%2F%28x-16%29%2B1%2Fx%29=%2815x%28x-16%29%29%281%2F15%29
15x%2B15%28x-16%29=x%28x-16%29
15x%2B15x-240=x%5E2-16x
30x-240=x%5E2-16x
x%5E2-16x-30x%2B240=0
x%5E2-46x%2B240=0
-
x=%2846%2B-sqrt%2846%5E2-4%2A240%29%29%2F2
x=%2846%2B-+sqrt%281156%29%29%2F2
x=%2846%2B-+34%29%2F2
system%28x=6%2Cor%2Chighlight%28x=40%29%29-----------time for B.

The time for A to do the job alone would be 40-16=highlight%2834%29 minutes.

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
You made a mistake in your way. The correct equation is 


1%2F%28x-16%29 + 1%2Fx = 1%2F15.     (I am sure you are able to identify your error on your own !)



Now, to solve it, multiply both sides by 15*x*(x-16). You will get

15x + 15(x-16) = x*(x-16),

15x + 15x - 240 = x%5E2+-+16x,

x%5E2+-+46x++%2B+240 = 0.     (1)

Factor left side polynomial:

(x-40)*(x-6) = 0

So, the equation (1) has two solutions: x= 40  and  x= 6.

Let us check both:


1)  x = 40 means B makes the job in 40 days. Then A makes it in 40-16 = 24 days.

    15%2A%281%2F40%2B1%2F24%29 = 15%2A%283%2F120+%2B+5%2F120%29 = 15%2A%288%2F120%29 = 1.   Correct !!


2)  x= 6 means B makes the job in 6 days. Then A makes it in 6-16 = -10 days.

    It doesn't make sense.


So, the only solution is this:

Answer. B can do the job in 40 days. A can do the job in 40 - 16 = 24 days.

Solved.


It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons

    - Rate of work problems
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Using quadratic equations to solve word problems on joint work (*)
    - Solving rate of work problem by reducing to a system of linear equations
    - Selected joint-work word problems from the archive
    - Joint-work problems for 3 participants
    - Had there were more workers, the job would be completed sooner
    - One unusual joint work problem
    - Joint work word problem for the day of April, 1
    - OVERVIEW of lessons on rate-of-work problems


Read them and get be trained in solving joint-work problems.
Problems in the lesson (*) are most closest to your problem.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".