SOLUTION: 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.

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.
---
Let the uniform width of the path around be "x".
----------
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"
=========================================================
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?
---------
8000 + 8000*2r + 2500 + 2500r
Equation:
8000(1+2r) + 2500(1+r) = 11445
Solve for "r"
=========================================================
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.
----
Original speed DATA:
distance = 150 miles ; rate = r mph ; time = d/r = 150/r hrs.
------------------
Increased speed DATA:
distance = 150 miles ; rate = (r+20) mph ; time = 150/(r+2) hrs
-------------------
Equation:
old time - new time = 2 hrs
150/r - (150/(r+20) = 2 hrs
Solve for "r"
============================

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?
--------------------
Upriver rate = b-5 ; distance = 40: time = 40/(b-5) hrs
Downriver rate = b+5 distance = 40; time = 40/(b+5) hrs
-------------
Equation:
40/(b-5) + 40/(b+5) = 6
Solve for b
===========================================================
Cheers,
Stan H.
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