Considering the least common factor of 15 and 18, it is found that they will depart from the central station at the same time at 11 AM.
<h3>How to find the time it takes for periodic events to repeat at the same time?</h3>
To find the time that passes between the events happening at the same time, we need to find the least common multiple of the periods.
In this problem, the periods are of 15 and 18, hence their lcm is found as follows:
15 - 18|2
15 - 9|3
5 - 3|3
5 - 1|5
1 - 1
Hence:
lcm(15,18) = 2 x 3 x 3 x 5 = 90 minutes.
They will depart from the central station at the same time in 90 minutes from 9:30 AM, hence at 11 AM.
More can be learned about the least common factor at brainly.com/question/16314496
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Answer:
(0,0) (-2,1) (-4,2) (-6,3) (-8,4)
Step-by-step explanation:
Hope this helps!
Answer:
or 
Step-by-step explanation:
Substitution means plugging in one variable's value that consists of the opposite variable. Because 
is already specified, you can plug it into the second equation's 
value. After doing that, it looks like this:
Then you would distribute the 
across the parentheses next to it, like this:
Then, add like terms, like this:
Then divide both side by 
to isolate 
.
Now, you can plug 
() into either equation, but the first one seems simpler so you would pick that. It would look like this:
Solving would look like this:
So the answer is or .
Answer:
x= The amount of lawns Mike mowed
y= The amount of lawns Chris Mowed
Equation 1: ($20+$15)(x+y)+$50=$500
Equation 2: ($20x)+($20xy)+$50=$500
Suppose the larger pump alone can empty the tank in L hours, and the smaller pump can finish the job in S hours, then each hour the large pump empties 1/L portion of the tank, and the small pump empties 1/S per hour
Working together for three hours, they empty the whole tank, which is 100% of it, so 3/L+3/S=100%=1
Larger pump can empty the tank in 4 hours less than the smaller one, so L=S-4
replace L: 3/(S-4)+3/S=1
Make the denominator the same to solve for:
3S/[S(S-4)] +3(S-4)/[S(S-4)]=1
(3S+3S-12)/[S(S-4)]=1
(3S+3S-12)=[S(S-4)]
S^2-10s+12=0
use the quadratic formula to solve for S
S is about 8.6
The answer is not whole hour.
