Jim's stride measures 2 1/2 feet, and Jeffrey's stride measures 2 2/3 feet. There are 5280 feet in a mile. If Jim and Jeffrey each walk one mile, what is the ratio of the number of strides Jim takes to the number of strides Jeffrey takes? Express your answer as a common fraction.

Logic
Aug 28, 2018

#1**+2 **

5280 ft / (2\(\frac12\) ft per stride) = 5280 ft / (2.5 ft per stride) = 2112 strides

So Jim must take 2112 strides to go exactly one mile.

num of strides Jim takes = 2112

5280 ft / (2\(\frac23\) ft per stride) = 5280 ft / (\(\frac83\) ft per stride) = 1983.75 strides

So Jeffrey must take 1983.75 strides to go exactly one mile.

num of strides Jeffrey takes = 1983.75

ratio of the num of strides Jim takes to the num of strides Jeffrey takes

= num of strides Jim takes / num of strides Jeffrey takes

= 2112 / 1983.75

= 211200 / 198375

= 2816 / 2645

However...

if Jeffrey cannot take a fraction of a stride, he must take 1984 strides to reach a mile. If so...

num of strides Jeffrey takes = 1984

And...

ratio of the num of strides Jim takes to the num of strides Jeffrey takes

= num of strides Jim takes / num of strides Jeffrey takes

= 2112 / 1984

= 33 / 31

hectictar
Aug 28, 2018

#1**+2 **

Best Answer

5280 ft / (2\(\frac12\) ft per stride) = 5280 ft / (2.5 ft per stride) = 2112 strides

So Jim must take 2112 strides to go exactly one mile.

num of strides Jim takes = 2112

5280 ft / (2\(\frac23\) ft per stride) = 5280 ft / (\(\frac83\) ft per stride) = 1983.75 strides

So Jeffrey must take 1983.75 strides to go exactly one mile.

num of strides Jeffrey takes = 1983.75

ratio of the num of strides Jim takes to the num of strides Jeffrey takes

= num of strides Jim takes / num of strides Jeffrey takes

= 2112 / 1983.75

= 211200 / 198375

= 2816 / 2645

However...

if Jeffrey cannot take a fraction of a stride, he must take 1984 strides to reach a mile. If so...

num of strides Jeffrey takes = 1984

And...

ratio of the num of strides Jim takes to the num of strides Jeffrey takes

= num of strides Jim takes / num of strides Jeffrey takes

= 2112 / 1984

= 33 / 31

hectictar
Aug 28, 2018