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Arte-miy333 [17]
3 years ago
14

The Price family and the Jenkins family each used their sprinklers last summer. The water output rate for the Price family's spr

inkler was 20L per hour. The water output rate for the Jenkins family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1200L. How long was each sprinkler used? URGENT!!!!
Mathematics
1 answer:
PIT_PIT [208]3 years ago
7 0

Set up two equations:

1st:  P (for Price family) + J (for Jenkins family) = 45 hours

2nd: 20P + 35J = 1200 liters

Rewrite the first equation as P = 45 – J

Replace P in the second equation:

20(45-J) + 35J = 1200

Simplify:

900 -20J + 35J = 1200

900 +15J = 1200

Subtract 900 from both sides:

15J = 300

Divide both sides by 15:

J = 300/15

J = 20

Jenkins used theirs for 20 hours

Price used theirs for 45-20 = 25 hours.

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<u>First, find the cost function of DoItRight Housekeeping:</u>

  • Slope(m) = cost per hour = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{44-26}{3-1.5}=\frac{18}{1.5}=12

<em>The y-intercept(b), representing the initial cost, can be calculated by substituting in values to the function:</em>

f(x)=12x+b\\26=12(1.5)+b\\b=26-18=8

<u>Therefore, the function for two companies are:</u>

  • The function for DoItRight is f(x)=12x+8
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When comparing the two functions, it's shown how CleanIt has a greater y-intercept than DoltRight, meaning that CleanIt has a greater initial cost than DotRight. The y-intercept is when the graph intercepts the y-axis, therefore, the coordinates there would be (0, y-value), which, in this case for CleanIt company, will be (0, 16). While CleanIt has a greater y-intercept(initial cost), DoItRight has a greater slope, meaning they cost more per hour.

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Please answer A S A P
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Answer:

1, i) equation for Mike's Repair Shop = $65x + $100

  ii) Amy's Auto Repair = $80x + $40

2. 65x + 100 = 80x + 40

3.  x = 4  

4. Therefore the number of hours at which the cost both auto repair shops are the same is x = 4 hours.

5. If it takes only three hours to fix the car the Amy' repair shop will be the cheapest because Amy's auto repair will cost = $80\times3 + $40 = $280 and Mike's will cost = $65\times3 + $100 = $295.

6. If it takes only six hours to fix the car the Amy' repair shop will be the cheapest because Amy's auto repair will cost = $80\times6 + $40 = $520 and Mike's will cost = $65\times6 + $100 = $490.

7. Amy's Auto repair service is advertising to encourage customers with quick repairs to use their service because their cost is less for quick repairs but more for lengthy repairs.

Step-by-step explanation:

i) x = number of hours worked

ii) y = total cost

1, i) equation for Mike's Repair Shop = $65x + $100

  ii) Amy's Auto Repair = $80x + $40

2. 65x + 100 = 80x + 40

3.   15x = 60, therefore x = 4  

4. Therefore the number of hours at which the cost both auto repair shops are the same is x = 4 hours.

5. If it takes only three hours to fix the car the Amy' repair shop will be the cheapest because Amy's auto repair will cost = $80\times3 + $40 = $280 and Mike's will cost = $65\times3 + $100 = $295.

6. If it takes only six hours to fix the car the Amy' repair shop will be the cheapest because Amy's auto repair will cost = $80\times6 + $40 = $520 and Mike's will cost = $65\times6 + $100 = $490.

7. Amy's Auto repair service is advertising to encourage customers with quick repairs to use their service because their cost is less for quick repairs but more for lengthy repairs.

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