Average Rates

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Average rates are quite like weighted average. You will be asked two or more questions related to this on your SAT exam so make sure not to fall for the common trap.

  • Sara drive to the supermarket takes her 20 minutes, throughout which she averages a speed of 21 miles per hour. She takes the same route home, but it only takes 15 minutes to cover the equivalent distance. Find the Sara’s average speed while driving?
    15.5 mph
    21 mph
    24 mph
    24.5 mph
    28 mph

Though this is a tricky and multi-step problem hence you can’t plug in the answer choices to solve it.

 

Let’s start with finding all the information as the question has given you only a part of it. Firstly, you need to know the following formula

r=d/t

(rate = distance/time)

 

We will use it both ways.

Now using this formula, let’s look at the first leg of her trip. As she traveled for 1/3 of an hour at 21 mph, so she must have traveled 7 miles.

21*0.333=7

Now using the above info, we can find out the rate of her trip back home. Going 7 miles in 1/4 of an hour on the way home, therefore she went an average of 28 mph.

7/0.25=28

Now we will find the total average. It’s not an average of the two numbers as the miles she traveled on the way are more time than to reach home. They have different weights.

✗ {21+28}/2=24.5

Don’t work like the above equation. The correct way is to take the total of each piece i.e. total time and total distance and then find the total average rate.

✓ {14 miles}/ {.333 hours + .25 hours} = {14 miles}/ {.5833 hours} = {24 mph}

Moreover, you will probably not see a question on SAT that will ask you to find an average based on percent weights. Let’s say, finding a final grade in a class where tests count for 60%, attendance 15% and class participation 25%. As finding an average in such situation is difficult so you don’t need to worry about it.

If you are required to figure out the average of two sets of information that already are averages as a number of fleas per cat and number of fleas per dog, you can’t simply take the mean of those averages. You need to find the totals and plug them into the formula.

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