Question

q10. rolando ran $2 \frac{5}{8}$ miles in $\frac{1}{2}$ hour. given that 1 mile = 1,760 yards, what was rolandos running rate in yards per hour? (1 point) a 4,620 yards per hour b 4,070 yards per hour c 2,310 yards per hour d 9,240 yards per hour

Explanation:

Step1: Convert mixed number to improper fraction

The distance Roland ran is \(2\frac{5}{8}\) miles. Convert this to an improper fraction: \(2\frac{5}{8}=\frac{2\times8 + 5}{8}=\frac{21}{8}\) miles.

Step2: Find distance in yards for \(\frac{1}{2}\) hour

Since 1 mile = 1760 yards, the distance in yards for \(\frac{21}{8}\) miles is \(\frac{21}{8}\times1760\) yards. Calculate this: \(\frac{21\times1760}{8}=21\times220 = 4620\) yards. This is the distance in \(\frac{1}{2}\) hour.

Step3: Find rate in yards per hour

To find the rate per hour, we know that in \(\frac{1}{2}\) hour he ran 4620 yards. So in 1 hour, the rate is \(4620\div\frac{1}{2}=4620\times2 = 9240\) yards per hour? Wait, no, wait. Wait, no, let's check again. Wait, no, the time is \(\frac{1}{2}\) hour, so to find per hour, we can also think: if he ran \(2\frac{5}{8}\) miles in \(\frac{1}{2}\) hour, then in 1 hour he runs \(2\times2\frac{5}{8}=2\times\frac{21}{8}=\frac{21}{4}=5\frac{1}{4}\) miles? Wait, no, that's not right. Wait, no, the first step: \(2\frac{5}{8}\) miles in \(\frac{1}{2}\) hour. So to find miles per hour, we do \(\frac{2\frac{5}{8}}{\frac{1}{2}}=\frac{21}{8}\times2=\frac{21}{4}=5.25\) miles per hour. Then convert miles to yards: \(5.25\times1760 = 5\times1760+0.25\times1760=8800 + 440 = 9240\) yards per hour. Wait, but the options have D as 9,240. Wait, but let's check the calculation again. Wait, \(2\frac{5}{8}\) is \(\frac{21}{8}\). \(\frac{21}{8}\) miles in \(\frac{1}{2}\) hour. So speed in miles per hour is \(\frac{21}{8}\div\frac{1}{2}=\frac{21}{8}\times2=\frac{21}{4}=5.25\) miles per hour. Then 5.25 miles times 1760 yards per mile: 5.251760. Let's calculate 51760=8800, 0.251760=440, so 8800+440=9240. So the rate is 9240 yards per hour. Wait, but the options: D is 9,240 yards per hour. Wait, but let's check the initial calculation. Wait, maybe I made a mistake. Wait, the problem says "Rolando ran \(2\frac{5}{8}\) miles in \(\frac{1}{2}\) hour". So to find yards per hour, first convert miles to yards for the distance he ran in \(\frac{1}{2}\) hour, then multiply by 2 (since \(\frac{1}{2}\) hour times 2 is 1 hour). So \(2\frac{5}{8}\) miles is \(\frac{21}{8}\) miles. \(\frac{21}{8}\times1760=\frac{21\times1760}{8}=21\times220 = 4620\) yards in \(\frac{1}{2}\) hour. Then per hour, it's 46202=9240 yards per hour. So the answer is D.

Answer:

D. 9,240 yards per hour