Question

1. The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 46 pounds when the spring is stretched 4 inches, find the tension when the spring is stretched twice as far.

2. The time t it takes to fill a bucket varies directly with the volume g of the bucket. If it takes 2 minutes to fill a 8-gallon bucket, how long will it take to fill a 5-gallon bucket?

3. The power P in an electric circuit varies directly with the square of the current I. If P = 30 when I = 2, find P when I = 5.

4. The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 28 hours and earns $137, how much does she make if she works 42 hours?

5. The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 250 pounds 4,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth.

Answer 1

9514 1404 393

Answer:

1. 92 pounds
2. 1 minute 15 seconds
3. 187.5
4. $205.50
5. 160 pounds

Step-by-step explanation:

1. The tension is proportional to distance, so twice the distance will result in twice the tension:

2 × 46 lbs = 92 lbs

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2. The fill time is proportional to the volume, so 5/8 of the volume will take 5/8 of the time:

(5/8)(2 min) = 10/8 min = 5/4 min = 1 minute 15 seconds

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3. When the current increases by a factor of 5/2, the power increases by the square of that factor.

(5/2)^2 × 30 = 187.5 . . . power at increased current

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4. Working 42/28 times as many hours will result in 48/28 times as much pay:

(42/28) × $137 = $205.50

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5. The new distance is 5000/4000 = 5/4 times the reference distance, so the new weight will be 1/(5/4)^2 = (4/5)^2 = 16/25 times the reference weight.

(16/25)(250 lbs) = 160 lbs