# Equations and word problems

Solve the following problems showing all your work every step of the way:

1. The following equation describes a person's optimum heart rate in beats per minute that should be achieved during exercise so that the exercise is most beneficial.

Heart rate = 0.6(220-a)

where a represents the age of the person in years.

Determine the optimum heart rate for a 35-year-old runner.

2. Research: One of the most famous formulas in the world was formulated by Albert Einstein. The formulas is E = mc2 . Use the library or the internet to research this formula and explain each variable and what the formula represents.

3. Write three different equations that have the solution of 5.

4. Set up the following problem as an equation and then solve. Tom's Rent-A-Heap Agency charges $150 per week plus $0.15 per mile to rent a small vehicle. How many miles can you travel for $550? Show your work.

In your own words, please post a response to the Discussion Board and comment on other postings. You will be graded on the quality of your postings.

(If you have any tips for me to get an understanding of math, I would be so grateful)!

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#### Solution Preview

The solution is below.

1. We are told the runner is 35 years old. So to get his optimum heart rate, we just need to substitute a=35 into the formula:

Optimum heart rate=0.6(220-35)=0.6(185)=111

2. This is the mass-energy equivalence formula. It describes the energy contained by a body by virtue of its mass.

E is the energy, measured in Joules.

m is the relativistic mass, measured in kilograms.

c is the speed ...

#### Solution Summary

This provides examples of using equations to solve word problems.

Differential Equations: Rate of Change Word Problem

Set up but do not solve a differential equation that models the amount of salt in the tank for the following: A tank, having a capacity of 700 liters, initially contains 3 kilograms of salt dissolved in 100 liters of water. At time t=0, a solution containing 0.4 kilograms of salt per liter flows into the tank at a rate of 3 liters/min and the well stirred moisture flows out at a rate of 2 liters/min. Be sure to define all of your variables.

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