Questions: On a typical work day, the trapeze artist spends 1 / 2 of his time plotting his jumps and 1 / 4 of his time hoping he won't fall. If the trapeze artist spends a total of 6 hours on these two activities, how many hours does he typically work each day?

On a typical work day, the trapeze artist spends 1 / 2 of his time plotting his jumps and 1 / 4 of his time hoping he won't fall. If the trapeze artist spends a total of 6 hours on these two activities, how many hours does he typically work each day?

Transcript text: On a typical work day, the trapeze artist spends $1 / 2$ of his time plotting his jumps and $1 / 4$ of his time hoping he won't fall. If the trapeze artist spends a total of 6 hours on these two activities, how many hours does he typically work each day?

Solution

Solution Steps

To find out how many hours the trapeze artist typically works each day, we need to determine the total fraction of his workday spent on these two activities and then use this to calculate the total work hours. The sum of the fractions of time spent on plotting jumps and hoping not to fall is $ \frac{1}{2} + \frac{1}{4} $. This sum represents the fraction of the total workday that equals 6 hours. We can set up an equation to solve for the total work hours.

Step 1: Determine the Total Fraction of Time Spent

The trapeze artist spends $ \frac{1}{2} $ of his time plotting jumps and $ \frac{1}{4} $ of his time hoping he won't fall. The total fraction of time spent on these activities is calculated as follows:

\[ \text{Total Fraction} = \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \]

Step 2: Set Up the Equation

Let $ T $ represent the total work hours in a day. The total time spent on the two activities is given as 6 hours, which can be expressed in terms of $ T $:

\[ \frac{3}{4} T = 6 \]

Step 3: Solve for Total Work Hours

To find $ T $, we rearrange the equation:

\[ T = 6 \div \frac{3}{4} = 6 \times \frac{4}{3} = 8 \]