Certainly! Let's solve the problem step-by-step with detailed explanations.
### Part (a)
Question: Emily drives 186 miles in 3 hours. What is her average speed?
Step-by-Step Solution:
1. Identify the distance Emily drove: The problem states that Emily drove 186 miles.
2. Identify the time Emily took: The problem states that Emily took 3 hours.
3. Formula for average speed: Average speed is calculated by dividing the total distance traveled by the total time taken.
[tex]\[
\text{Average speed} = \frac{\text{Distance}}{\text{Time}}
\][/tex]
4. Plug in the values:
[tex]\[
\text{Average speed} = \frac{186 \text{ miles}}{3 \text{ hours}} = 62 \text{ mph}
\][/tex]
Answer: Emily's average speed is 62 mph.
### Part (b)
Question: Sarah drives at an average speed of 58 mph for 4 hours. How many miles does she drive?
Step-by-Step Solution:
1. Identify the average speed Sarah is driving: The problem states that Sarah is driving at an average speed of 58 mph.
2. Identify the time Sarah drove: The problem states that Sarah drove for 4 hours.
3. Formula for distance traveled: Distance is calculated by multiplying the average speed by the time.
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
4. Plug in the values:
[tex]\[
\text{Distance} = 58 \text{ mph} \times 4 \text{ hours} = 232 \text{ miles}
\][/tex]
Answer: Sarah drives 232 miles.
