To solve this problem, we need to find the average speed of the cyclist over her ride.
Part A
Estimate the Quotient: To estimate the average speed, we can simplify the division. We know she rode 60.9 miles in 3.5 hours. To estimate, we can round these numbers:
- Round 60.9 to 61 (approximately)
- Round 3.5 to 4 (approximately)
Now, we can set up the equation:
\[ \text{Estimated Speed} = \frac{\text{Estimated Distance}}{\text{Estimated Time}} = \frac{61 \text{ miles}}{4 \text{ hours}} = 15.25 \text{ miles per hour} \]
By estimating, we can see that the cyclist rode approximately 15.25 miles in an hour. This helps us understand that her speed is around this value, but we will need to find the exact answer in Part B.
Part B
Find the Exact Distance She Rode in 1 Hour: Now, let's perform the exact division:
\[ \text{Average Speed} = \frac{60.9 \text{ miles}}{3.5 \text{ hours}} \]
To make the division easier, we can convert 3.5 into a fraction:
\[ 3.5 = \frac{7}{2} \]
Now we can rewrite the division as:
\[ \frac{60.9}{3.5} = 60.9 \div 3.5 = 60.9 \times \frac{2}{7} \]
Calculating this gives:
\[ = \frac{60.9 \times 2}{7} = \frac{121.8}{7} \]
Now, performing the division:
\[ 121.8 \div 7 \approx 17.4 \]
Thus, the exact distance she rode in 1 hour is:
17.4 miles
So the answers are:
- Estimate from Part A: Approximately 15.25 miles per hour
- Exact answer for Part B: 17.4 miles.