Question 995694
ryan runs faster.


here's my worksheet that confirms it for all ryan rates that are valid.


in this workbook:


x represnet ryans rate per kilometer.


the results are valid for all of ryan's rates greater than 1 kmph.


at 1 kmph, the results are not valid because there is a division by 0.


at less than 1 kmph, the results are invalid because sophie's rates becomes negative.


the formulas used are:


let x = ryan's rate.


rate * time = distance


distance = 4 km.


formula becomes:


x * time = 4


ryan's time = 4 / x


sophie's time is calculated as follows:


sophie's time for first 2 km is equal to 2 / (x+1)


sophie's time for second 2 km is equal to 2 / (x-1)


sophie's time for all 4 km is 2/(x+1) + 2/(x-1)


results are shown below:


div/0 means the results are invalid because there has been a division by 0.


<img src = "http://theo.x10hosting.com/2015/101101.jpg" alt="$$$" </>