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?

2 Answers
Oct 29, 2017

#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

Oct 30, 2017

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