Question

A young lady walks home from a friend's house. After 2 minutes she is 0.8 miles from home. After 12 minutes she is 0.3 miles from home. What is her walking speed in miles per hour?

Answer 1

`3` mph

Explanation:

After `2` minutes, she is `0.8` miles from home. After `12` minutes, she is `0.3` miles from home.

Therefore, we can see that she has traveled:

`0.8 - 0.3 = 0.5` miles
`12 - 2 = 10` minutes

`0.5` miles in `10` minutes.

They want the answer in miles per hour, so we need to convert 10 minutes to 1 hour (60 minutes):

`10 * 6 = 60` minutes (`1` hour)

Therefore, we must also multiple the miles traveled by 6:
`0.5 * 6 = 3` miles

After converting, you can now see that she has traveled `3` miles in `1` hour, so we write our answer using the correct units:

`3` mph

Answer 2

3 miles per hour

Explanation:

`("distance")/("time") color(white)("d")->color(white)("ddd")(0.8" miles from home")/(2" minutes") larrcolor(brown)(1^("st")" relationship")`

`("distance")/("time") color(white)("d")->color(white)("ddd")(0.3" miles from home")/(12" minutes") larrcolor(brown)(2^("nd")" relationship")`

So speed (velocity) is:

`("distance traveled")/("time") =(0.8-0.3)/(12-2) = (0.5" miles")/(10" minutes")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
But we need the count of miles for 1 hour. So we need to change the 10 minutes into 1 hour `->` 60 minutes

`color(brown)("Multiply by 1 and you do not change the value. However, 1")` `color(brown)("comes in many forms.")`

`color(green)(0.5/10color(red)(xx1)color(white)("d")=color(white)("d") 0.5/10color(red)(xx6/6)`

`color(white)("ddddddd")=color(white)("d")(3.0" miles")/(60" minutes")`

But 60 minutes is the same as 1 hour. so by substitution in the denominator we have:

`color(white)("ddddddd")=color(white)("d")(3.0" miles")/(1" hour")`

So the speed (velocity) is 3 miles per hour