Question 186289This question is from textbook Elementary and Intermediate Algebra
: If there is any way you can help, please do, I am soooo lost.
Show the equation that you used to solve each problem. Be sure to say what quantity each variable represents.
1. A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?
This question is from textbook Elementary and Intermediate Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
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Draw the picture of a rectangle inside a rectangle.
Dimensions of the inner rectangle are 15 and 11.
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Let the uniform width of the path around be "x".
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Dimensions of the outer rectangle are (15+2x) and (11+2x)
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The area of the path is [(15+2x)(11+2x)-15*11]
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Equation: [(15+2x)(11+2x)-15*11] = 192
solve for "x"
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2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
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8000 + 8000*2r + 2500 + 2500r
Equation:
8000(1+2r) + 2500(1+r) = 11445
Solve for "r"
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3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
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Original speed DATA:
distance = 150 miles ; rate = r mph ; time = d/r = 150/r hrs.
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Increased speed DATA:
distance = 150 miles ; rate = (r+20) mph ; time = 150/(r+2) hrs
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Equation:
old time - new time = 2 hrs
150/r - (150/(r+20) = 2 hrs
Solve for "r"
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4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?
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Upriver rate = b-5 ; distance = 40: time = 40/(b-5) hrs
Downriver rate = b+5 distance = 40; time = 40/(b+5) hrs
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Equation:
40/(b-5) + 40/(b+5) = 6
Solve for b
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Cheers,
Stan H.
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