Raul biked at a steady speed during his 8-mile ride. He finished the ride in (4)/(5) hour. Which fraction represents Raul’s speed in miles per hour? (4)/(5) (4)/(5) (8)/(5) (8)/((4)/(5))
The Correct Answer and Explanation is:
Let’s analyze the problem step-by-step:
Problem:
Raul biked 8 miles in 45\frac{4}{5}54 hour. We need to find his speed in miles per hour as a fraction.
Step 1: Understand what speed means
Speed is calculated as: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed=TimeDistance
Raul traveled 8 miles in 45\frac{4}{5}54 hour, so his speed sss is: s=8 miles45 hours = \frac{8 \text{ miles}}{\frac{4}{5} \text{ hour}}s=54 hour8 miles
Step 2: Divide by a fraction
Dividing by a fraction is the same as multiplying by its reciprocal: s=8×54s = 8 \times \frac{5}{4}s=8×45
Step 3: Simplify the multiplication
Multiply numerators and denominators: s=8×54=404=10s = \frac{8 \times 5}{4} = \frac{40}{4} = 10s=48×5=440=10
Step 4: Express as a fraction
The speed is 10 miles per hour. In terms of fractions given as options, the one that matches the operation is: 845\frac{8}{\frac{4}{5}}548
This expression represents dividing 8 by 45\frac{4}{5}54, which is how you calculate speed.
Summary:
- The correct fraction representing Raul’s speed is 845\frac{8}{\frac{4}{5}}548.
- Simplifying this gives 10 miles per hour.
Explanation
To find Raul’s speed in miles per hour, we need to remember the basic formula for speed: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}Speed=TimeDistance
Here, Raul rode 8 miles in 45\frac{4}{5}54 hour. This means the total distance traveled was 8 miles and the total time taken was four-fifths of an hour.
We need to divide 8 miles by 45\frac{4}{5}54 hour. Dividing by a fraction can be tricky if you’re not familiar with the rules, but the key idea is to multiply by the reciprocal of the fraction.
The reciprocal of 45\frac{4}{5}54 is 54\frac{5}{4}45, so: 845=8×54\frac{8}{\frac{4}{5}} = 8 \times \frac{5}{4}548=8×45
When you multiply 8 by 54\frac{5}{4}45, you multiply the numerators and divide by the denominator: 8×54=8×54=404=108 \times \frac{5}{4} = \frac{8 \times 5}{4} = \frac{40}{4} = 108×45=48×5=440=10
Therefore, Raul’s speed is 10 miles per hour.
Among the answer choices, the expression 845\frac{8}{\frac{4}{5}}548 correctly shows the operation needed to find speed. The other options, like 45\frac{4}{5}54 or 85\frac{8}{5}58, do not correctly represent the speed.
This method reflects the real-world concept that when you cover a certain distance in less than one hour, your speed will be greater than that distance because the time is less than one hour (since 45<1\frac{4}{5} < 154<1).
Final answer: 845\boxed{\frac{8}{\frac{4}{5}}}548
