Brock Obama, Justin Trudeau and Jinping Xi decide to help Mr Blakely bathe
his super cat Mike Wazowski. Brock can bathe Mike Wazowski in x minutes, Justin
can bathe it in 2 minutes less than Brock, and Jinping can bathe it in 2 minutes
more than Brock. When Brock and Justin worktogehe, they take 10 minutes to
bathe the cat. When Justin and Jinping work together, it takes 12 minutes to
bathe the cat.
a) How long does each president take to bathe Mike Wazowski?
b) How long would all three of them, working together, take to bathe Mike
I really have no idea how to solve this question. I just know that the two equations are gonna be
1/x + 1/x-2 = 10
1/x-2 + 1/x+2 = 12
a) (10 / x) + [10 / (x-2)] = 1
10x - 20 + 10x = x^2 - 2x
0 = x^2 - 22x + 20
use quadratic equation to find x
b) (t / x) + [t / (x-2)] + [t / (x+2)] = 1
For a wouldn't the equation be -1(x^2 + 18x + 20) ??
Nevermind I understand now, thank you!
This question makes no sense.
let Brock take x minutes,
then Justin takes x-2 minutes,
Jinping takes x+2 minutes
first case:
1/x + 1/(x-2) = 1/10 , (you had 10 on the right side)
This equation alone is sufficient to find x
.... multiply each term by 10x(x-2)
10(x-2) + 10x = x(x-2)
10x - 20 + 10x = x^2 - 2x
x^2 - 22x + 20 = 0
this gives a solution of 21.05 and .95
We have to reject the 2nd answer since it would give us a negative time for Justin.
So Brock takes 21.05 minutes alone, and Justin takes 19.05 minutes alone
check: their combined rate is 1/21.05 + 1/19.05 = .0999993..
and the time at that combined rate is 1/.099993...
= 10.000006...
which is the given time
So Ok so far,
but that contradicts the information for the combined times for Justin and Jin
which would have a combined rate of
1/19.05 + 1/ 23.05 = .095877..
and the time at that combined rate is 1/.095877.. = appr 10.43
and not 12 minutes.
So we have conflicting information.
another way to show the inconsistency of this question is to solve the second equation:
1/(x-2) + 1/(x+2)= 1/12, which would give x = 24.166
different from the first x value
Whoever made up this question spent more time trying to be cute than planning out the math.
To solve this problem, we can use the given information to create a system of equations and solve for the unknowns.
Let's start by assigning variables to the unknowns:
Let x represent the time it takes for Brock Obama to bathe Mike Wazowski.
Then, Justin Trudeau takes x - 2 minutes, and Jinping Xi takes x + 2 minutes.
Now, we can set up the equations:
1. When Brock and Justin work together, it takes them 10 minutes to bathe the cat:
In this case, we can combine their individual rates of work to find the combined rate when working together. The equation would be:
1/x + 1/(x - 2) = 1/10
2. When Justin and Jinping work together, it takes them 12 minutes to bathe the cat:
Again, we can set up a similar equation:
1/(x - 2) + 1/(x + 2) = 1/12
Now, we have a system of equations:
Equation 1: 1/x + 1/(x - 2) = 1/10
Equation 2: 1/(x - 2) + 1/(x + 2) = 1/12
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
Multiply both sides of Equation 1 by 12(x)(x - 2) to get rid of the denominators:
12(x - 2) + 12x = x(x - 2)
Simplifying the equation:
12x - 24 + 12x = x^2 - 2x
24x - 24 = x^2 - 2x
Rearrange the equation:
x^2 - 26x + 24 = 0
Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Factoring this equation might not be straightforward. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Applying the quadratic formula with a = 1, b = -26, and c = 24:
x = (-(-26) ± sqrt((-26)^2 - 4(1)(24))) / (2(1))
Simplifying:
x = (26 ± sqrt(676 - 96)) / 2
x = (26 ± sqrt(580)) / 2
x = (26 ± 2sqrt(145)) / 2
x = 13 ± sqrt(145)
Since we are dealing with time, the negative value does not make sense in this context. So, let's ignore the negative value.
x = 13 + sqrt(145)
This gives us the solution for the time it takes Brock Obama to bathe Mike Wazowski.
Now, we can find how long Justin Trudeau and Jinping Xi take using the given information:
Justin Trudeau = x - 2 = 13 + sqrt(145) - 2
Jinping Xi = x + 2 = 13 + sqrt(145) + 2
So, the answers to part (a) are:
- Brock Obama takes 13 + sqrt(145) minutes.
- Justin Trudeau takes 11 + sqrt(145) minutes.
- Jinping Xi takes 15 + sqrt(145) minutes.
To calculate part (b), we need to find the rate at which all three presidents work together. We can combine their individual rates and set it equal to 1 over the total time taken (let's call it T):
(1 / (13 + sqrt(145))) + (1 / (11 + sqrt(145))) + (1 / (15 + sqrt(145))) = 1/T
Now, we can solve this equation to find the value of T, which will give us the time taken when they all work together. However, since the equation involves irrational numbers, solving it algebraically might be challenging. It would be more practical to use numerical methods or a calculator to approximate the value of T.