An agricultural irrigation system uses two types of sprinklers, Type A and Type B. Water f… — SAT

An agricultural irrigation system uses two types of sprinklers, Type A and Type B. Water flows through $3$ Type A sprinklers at a combined rate of $15$ gallons per minute. Water flows through $5$ Type B sprinklers at a combined rate of $18$ gallons per minute. If a farmer runs $8$ Type A sprinklers and $10$ Type B sprinklers simultaneously, what is the total rate of water flow, in gallons per minute?

Answer: 76 gallons per minute

Answer

The total rate of water flow is 76 gallons per minute.

To find the total water flow rate, determine the rate of a single sprinkler of each type first. For Type A, the rate is

15 \text{ gallons per minute} \div 3 = 5 \text{ gallons per minute}

. For Type B, the rate is

18 \text{ gallons per minute} \div 5 = 3.6 \text{ gallons per minute}

. Running

8

Type A sprinklers and

10

Type B sprinklers simultaneously yields a total rate of

(8 \times 5) + (10 \times 3.6) = 40 + 36 = 76

gallons per minute.

Step-by-Step Solution

Find the rate of water flow for a single Type A sprinkler.

Each Type A sprinkler has a water flow rate of

5

gallons per minute.

Dividing the combined rate of

15

gallons per minute by the

3

sprinklers gives the individual rate.

Find the rate of water flow for a single Type B sprinkler.

Each Type B sprinkler has a water flow rate of

3.6

gallons per minute.

Dividing the combined rate of

18

gallons per minute by the

5

sprinklers gives the individual rate.

Calculate the total water flow rate for the combined group of active sprinklers.

The total combined flow rate is

76

gallons per minute.

Multiplying the individual rate of each type by the respective count of active sprinklers and summing the results:

(8 \times 5) + (10 \times 3.6) = 40 + 36 = 76

Key Concept

Combining rates of individual components to find a total rate.

Estimated Time:1m 30s

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