Kelly is knitting a scarf for her brother. It took 1/3 hour to knit 3/8 of a foot of the scarf. How fast is Kelly’s knitting speed, in feet per hour?
The correct answer and explanation is:
To find Kelly’s knitting speed in feet per hour, we divide the amount of scarf she knitted (in feet) by the time it took her (in hours).
Step-by-Step Solution:
- Kelly knitted 3/8 foot of scarf in 1/3 hour.
- Knitting speed is calculated as:
Speed=DistanceTime=3/81/3\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{3/8}{1/3}
To divide fractions, multiply by the reciprocal of the divisor: 38÷13=38×31=98\frac{3}{8} \div \frac{1}{3} = \frac{3}{8} \times \frac{3}{1} = \frac{9}{8}
So, Kelly’s knitting speed is 9/8 feet per hour, or 1.125 feet per hour.
Final Answer:
9/8 feet per hour or 1.125 feet per hour
Explanation (300 words):
This problem is a classic example of a rate or speed problem, where we are given the amount of something completed (in this case, scarf length in feet) and the time it took (in hours). The goal is to determine how much Kelly can knit in one hour based on that data.
We’re told she knits 3/8 of a foot in 1/3 of an hour. To find a rate in “feet per hour”, we divide the amount she knits (3/8 foot) by the time it takes (1/3 hour). This is a division of two fractions. When dividing by a fraction, we multiply by its reciprocal. The reciprocal of 1/3 is 3/1.
So: 38÷13=38×31=98\frac{3}{8} \div \frac{1}{3} = \frac{3}{8} \times \frac{3}{1} = \frac{9}{8}
This means she knits 9/8 of a foot every hour. You can also think of it this way: If she knits 3/8 foot in 1/3 hour, then in one full hour, she would have done that 3 times (since 3 × 1/3 = 1 full hour), so: 3×38=983 \times \frac{3}{8} = \frac{9}{8}
This verifies our calculation. Therefore, Kelly’s knitting speed is 9/8 feet per hour, or 1.125 feet per hour in decimal form. This kind of math is often used to understand efficiency or rates in real-life tasks.