Double Unit Conversions

This is a typical double unit conversion problem in 7th grade that asks students to convert between two “rates”.

If Mike is traveling at 60 miles per hour and Pete is traveling at 95 feet per second. Who is traveling faster? In feet per second, how much faster is he going?

Solution

We usually present the solution in this manner:

In 1 hour, Mike travels 60 miles = 5,280 x 60 = 316,800 feet
In 3600 seconds, Mike travels 316,800 feet
In 1 second, Mike travels 316,800 divided by 3600 = 88 feet

Mike’s speed is 88 feet per second
Pete’s speed is 95 feet per second

Therefore, Pete is faster
95 – 88 = 7

Pete is faster than Mike by 7 feet per second.

Discussion

We see that a rate quantity is actually a ratio between two measurement units, in this case, a distance measurement and a time duration measurement. Double unit conversion is an extension of what we’ve learned in Ratios and Proportion, where we deal only with conversions between two single-dimension quantities, e.g. ratio between 2 yards and 60 inches. It is just that now, we need to convert both dimensions to the same units before comparing, e.g. miles to feet and hours to seconds.

And just as before, when dealing with double unit conversions, it is important to note that units on both sides of the equality sign are different. That is 60 miles per hour is equivalent to 88 feet per second and yet the ratio 60:1 is not equivalent to 88:1. That is, 60/1 ≠ 88/1, but

60 [miles per hr] = 88 [ft per sec].

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