Question

a) Kyle walks 1/2 mi in each 1/4 of an hour. Use a complex fraction to find how many miles he walks per hour.b) find your answer to part a) by multiplying by the LCM of the denominators. Did you get the same answer? If not, find your mistake

Answer 1

a)

In order to find Kyle's speed in miles per hour, we just need to divide the amount of miles he walked by the amount of time it took:

`\text{speed}=((1)/(2))/((1)/(4))=(1)/(2)\cdot4=2\text{ mph}`

b)

In order to calculate the LCM of 2 and 4, let's factor them in their prime factors:

`\begin{gathered} 2\to2 \\ 4\to2\cdot2 \end{gathered}`

The LCM is the product of each prime factor the maximum number of times they appear in a single number, so we have LCM = 2 * 2 = 4.

Multiplying 1/2 and 1/4 by 4, we have:

`\begin{gathered} (1)/(2)\cdot4=2\text{ miles} \\ (1)/(4)\cdot4=1\text{ hour} \end{gathered}`

So in one hour he walks 2 miles, so his speed is 2 miles per hour.