How to Solve Rate Problems

Rate problems come down to fairly simple algebra.
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Rate problems are a staple of standardized tests, especially in college entrance exams like the SAT and ACT. A rate problem is usually a word problem where two variables are defined and a third variable is asked for. Some rate problems become more complicated by comparing two rates, thus doubling the number of variables. All rate problems can be solved by using the formula D = R(T), which translates to distance (D) equals rate (R) multiplied by time (T).

Draw a Variable Grid

    Draw a table with four columns and three rows.

    Label the columns in the first row with "Name," "Distance," "Rate" and "Time."

    Read the problem and identify which of the two things' rates are being compared. If more than two rates are involved, draw additional rows as necessary. If one rate is mentioned, just use the first row. Label each row in the first column with the name of the things.

    Convert any given numbers to be in matching units. If one speed is in miles per hour and another is in feet per second, pick which unit you want to work with and convert the other amount to use that unit.

    Plug any given numbers into the grid. Create a variable for any missing figures. Use "d" for distance, "r" for rate and "t" for time.

    Circle the part of the grid the question is asking for. This is the variable you eventually want to solve for.

Use the Rate Equation to Solve

    Take each row and rewrite it as D = R(T) beneath the grid, with the appropriate numbers or variables in place of D and R and T.

    Simplify each equation as much as possible. If only one variable is present, solve for it using basic algebra.

    Plug in any solved variable to solve further. If you haven't reached your answer in Step 2, take any solved variable and insert it into the other equation, then keep solving.