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
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
4 answers
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.
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.