Alex takes 3 hours longer to complete a certain job than Barry does. If they can complete the job
by working together in 3.6 hours, how long would it take Alex to complete the job working
alone?
3.
Immediately assign variables to the time that Alex and Barry take to do the job. Say the time Alex takes is a, and the time that Barry takes is b.
Thus, a = b + 3
You need to add 3 to the time of Barry so that the time of both persons are equal. (eg. if Alex takes 5 hours, Barry would take 2 hours and a = b + 3 would work because 5 = 2 + 3)
If they can complete the job by working together in 3.6 hours, how long would it take Alex to complete the job working alone?
This is where a handy little formula can be used. For things like that (time taken to so something alone and time taken to so the same thing with other people), you can use this:
T is the time they take if they work together. Say there was another person Cyrus also working, and c were the time he usually takes alone to complete the job, then you could still use the formula, but like this:
It's easy, right?
Now, you've got:
and
Simultaneous equations, solve for a
AAAAAAAAAAAHHH it didn't post right
1/b + 1/(b+3) = 1/3.6
or
1/b + 1/(b+3) = 5/18
18(b+3) + 18(b) = 5(b)(b+3)
18b + 54 + 18b = 5b^2 + 15b
5b^2 - 21b - 54 = 0
(5b+9)(b-6) = 0
b = 6
so,
a = 9
1/6 + 1/9 = (3+2)/18 = 5/18
To find the amount of time it would take Alex to complete the job working alone, we can set up an equation based on the given information.
Let's denote the time it takes Barry to complete the job as "x" hours. According to the problem, Alex takes 3 hours longer than Barry, so the time it takes Alex to complete the job would be "x + 3" hours.
Now, we need to find the total work done by both Alex and Barry when they work together for 3.6 hours. We can use the formula:
(1 / Alex's time) + (1 / Barry's time) = (1 / time when working together)
Plugging in the values we have:
(1 / (x + 3)) + (1 / x) = 1 / 3.6
To solve this equation, we can multiply all terms by (x + 3) * x * 3.6 to eliminate the denominators:
(3.6 * x) + (3.6 * (x + 3)) = (x + 3) * x
Expanding and simplifying:
3.6x + 3.6x + 10.8 = x^2 + 3x
Combining like terms:
7.2x + 10.8 = x^2 + 3x
Rearranging to form a quadratic equation:
x^2 - 4.2x + 10.8 - 3x - 10.8 = 0
x^2 - 7.2x = 0
Factoring out x:
x(x - 7.2) = 0
Setting each factor to zero and solving for x:
x = 0 or x - 7.2 = 0
Since time cannot be negative, we discard x = 0. Therefore, x - 7.2 = 0, which means x = 7.2.
So, it takes Barry 7.2 hours to complete the job alone. And since Alex takes 3 hours longer than Barry, we add 3 to Barry's time:
x + 3 = 7.2 + 3 = 10.2
Therefore, it would take Alex approximately 10.2 hours to complete the job working alone.