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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.

Aug 28, 2018

#1
+7598
+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

Aug 28, 2018

#1
+7598
+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