Monday, November 1, 2010

Converting Units - It's a One Step Process

Multiple units used for the same quantity in a question is an irritant to most of us. Today, I will discuss how to quickly convert from one to another so that we can focus on the actual question rather than getting lost in the units!

I will show how to do it using a couple of examples.

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)

In this question, I know her speed is 90 miles/2 hours. I need it in feet/second because distance is given in feet (which is 132 feet) and the answer is asked in seconds.

In place of 1 mile, we simply write 5280 feet and in place of 1 hour, we write 3600 seconds. (We know 1 hour has 60 minutes and 1 minute has 60 seconds, therefore, 1 hour has 60 x 60 = 3600 seconds). Voila! The whole thing has got converted to feet/sec.

We get that Jodie's speed is 66 feet/sec. Now, to solve the question we can simply use the Time-Speed-Distance formula which is, Time = Distance/Speed = 132 feet/66 feet per sec = 2 secs.

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)

Here we have Julia's speed in feet/sec and we need to convert it to miles/hour.
If 1 mile = 5280 feet, then 1 foot = 1/5280 miles and if 1 hour = 3600 seconds, then 1 second = 1/3600 hours

Now, using the Time-Speed-Distance formula again, Distance = Speed x Time = 90 miles/hour x 2 hours = 180 miles

Note: The units are also a part of the equation. We just don't notice them. For example, given below is what happens when we use the formula above,

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