I need a math wizard! What is wrong with the dimensional analysis work in the following problem in which 5 feet/second was converted to miles per hour?

Question

matt6288 · Answer

5feet/second was converted to miles per hour? 5feet/1second*1mile/5280feet*1minute/60s… ≈ 0.0001 miles per hour.

matt6288 · Answer

A.
    In the first conversation ratio, the second should be on top and the feet should be on bottom.
    B.
    In the second conversation ratio, the feet should be on top and the mile should be on bottom.
    C.
    In the third conversion ratio, the seconds should be on top and the minutes should be on the bottom.
    D.
    In the fourth conversation ratio, the hour should be on top and the minutes should be on bottom.

amistre64 · Answer

$$\frac{ft}{sec}\frac{sec}{min}\frac{min}{hr}=\frac{ft}{hr}$$

$$\frac{ft}{hr}\frac{mile}{ft}=\frac{mile}{hr}$$

amistre64 · Answer

or some versions of that

amistre64 · Answer

so the min/sec that they have is not a healthy operation

matt6288 · Answer

so it would be A?

amistre64 · Answer

hard to tell, that last bit needs to be an sec/hr i believe

amistre64 · Answer

5feet  1mile  1minute
sec       feet       sec


is what they got

so feet are off the top and we got mile/sec  we need sec/hr to finish up

amistre64 · Answer

the third conversion ... hard to count them, is whats bad at any rate

amistre64 · Answer

is ft/sec the 1st conversion or the is it not counted as a conversion?

amistre64 · Answer

ok, it reads as the first; so C is your best pick.  oy that was torture :)

matt6288 · Answer

Thx :)