Unit Conversion | Arithmetic

There is no running away from the reality that various units of measurement are used for the same physical quantity, so you will occasionally need to convert one to the other. Let us learn how to do it quickly and efficiently through the use of some examples similar to GMAT-questions.

Example 1: Jodie runs her Prius 90 miles in two hours. In how many seconds, does she cover 132 feet? (Given 1 mile = 5280 feet)

Solution: The solution involves two steps: First one makes the units consistent and second one solves for time. We know Jodie covers 90 miles in 2 hours so her speed is 45 mph. We need to convert her speed from miles/hour to feet/second because distance is given in feet and the answer needs the time in seconds.

$Speed\ =\ \frac{45\ miles}{1\ hour}=\ \frac{45 \times 5280\ feet}{3600\ seconds}=\frac{66\ feet}{second}$

Replace a mile by 5280 feet (because 1 mile = 5280 feet) and 1 hour by 3600 seconds (1 hour has 60 x 60 = 3600 seconds) in the expression. We get Jodie’s speed in feet/sec. Now, to solve the question, we simply use the Time-Speed-Distance formula which is,

$Time\ Taken=\ \frac{Distance}{Speed}=\ \frac{132\ feet}{66\ feet/sec}=2\ sec$

The solution to the above problem comes naturally to most people. They may not follow these same steps but nevertheless, they do not find it intimidating. In that respect, I haven’t added any value yet. But what is important here is the procedure because it can be helpful in solving problems that are a little spooky for some. Let me explain by taking a trickier example:

Example 2: Julia drives at a speed of 132 feet/sec. How many miles away is she from her home, if it will take her 2 hours to reach home? (Given 1 mile = 5280 feet)

Solution: Here we have Julia’s speed in feet/sec and we need to convert it to miles/hour because the distance asked is in miles and the time taken is in hours.

Given 1 mile = 5280 feet, it follows that 1 foot $= \frac{1}{5280}$ miles.