SOLUTION: Please help me solve this word problem: (show all working out please, Thanks) In a race over 4km Ryan ran at a constant speed. However, Sophie ran at the first 2 km at a speed o

Question 995694: Please help me solve this word problem: (show all working out please, Thanks)
In a race over 4km Ryan ran at a constant speed. However, Sophie ran at the first 2 km at a speed of 1km/h more than Ryan and ran the second 2km at a speed of 1km/h less than Ryan. Who won the race?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

$$$

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