This morning, as Diane drove to work, there was an accident that slowed down traffic. Diane made the 11-mile trip in 29 minutes. By the time she drove home, the accident had cleared and she took the same route home in just 12 minutes. What was Diane's average speed overall?

Question

Write your answer as a whole number or as a decimal rounded to the nearest tenth.

Answer 1

To find Diane's overall average speed, we first need to calculate the total distance she traveled and the total time it took.

Step 1: Calculate total distance.

Diane drove 11 miles to work and 11 miles back home:

\[ \text{Total distance} = 11 \text{ miles} + 11 \text{ miles} = 22 \text{ miles} \]

Step 2: Calculate total time.

Diane took 29 minutes to drive to work and 12 minutes to drive home:

\[ \text{Total time} = 29 \text{ minutes} + 12 \text{ minutes} = 41 \text{ minutes} \]

Step 3: Convert total time to hours.

Since speed is usually measured in miles per hour (mph), we convert the total time from minutes to hours:

\[ 41 \text{ minutes} = \frac{41}{60} \text{ hours} \]

Step 4: Calculate average speed.

Average speed is calculated using the formula:

\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]

Substituting our values:

\[ \text{Average speed} = \frac{22 \text{ miles}}{\frac{41}{60} \text{ hours}} = 22 \text{ miles} \times \frac{60}{41} = \frac{1320}{41} \text{ mph} \]

Step 5: Perform the division.

Calculating the division:

\[ \frac{1320}{41} \approx 32.3171 \]

Step 6: Round to the nearest tenth.

Rounding 32.3171 gives approximately 32.3.

Final Answer: Diane's average speed overall was 32.3 mph.