Question

Joseph walks 10 times around the track at a rate of x laps per hour. She runs eight times around the track of a rate of 3X laps per hour. Write and simplify an expression for the total time it takes him to go around the track 18 times

Answer 1

The expression for the total time is:

T =  (324/34x).

How to get the expression?

He does 18 laps in total.

• 8 laps at a rate of 3x
• 10 laps at a rate of x.

The average rate for the whole 18 laps is the average of the rates (taking in account the number of laps made with each) so we get:

average rate = (8/18)*3x + (10/18)*x = (34x/18)

This means that he does (34x/18) laps per hour.

Then, the time needed to do 18 laps is:

T = (18/(34x/18)) = (324/34x).

If you want to learn more about rates:

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