The Average Speed

SAT Math Tutorial

The Average Speed

Intro

The SAT tends to trick students into quickly answering a question that looks too familiar. For example they ask about averages and the knee-jerk response is to add the values and divide by the quantity of elements. This does not work for rates (for example: speed).

Sample Problem

Mary drives to her parent’s house at an average speed of 30 miles per hour. On her way back, Mary drives back to her house at a speed of 60 miles per hour. What’s Mary’s average speed for both trips?

Solution

The way to average rates is to get the total distance traveled and the total time and then dividing both. In this problem, we are not given the distance nor the time but this doesn’t mean we cannot solve the problem.

At this point, we have to know what we’re given. We are given 2 speeds (rates) and we’re also told that the distance traveled is the same.

The trick to solving this problem is assume a certain distance traveled. let’s assume the distance traveled from Mary’s home to her parents is 60 miles.

If one way is 60 miles, this mean the total distance is 60 x 2 = 120 miles (Mary went to her parent’s house and drove back).

If one way is 60 miles, we can use her speed to get the time it took her to get her parent’s house and back. We can get the time by dividing the distance (miles) by the speed (miles/hour)
– First trip: (60 miles) / (30 miles / hour) = 2 hours
– Second trip: (60 miles) / (60 miles / hour) = 1 hour
– Adding both trips, gives us the total time: 2 hours + 1 hour = 3 hours

Now we have the total time (3 hours) and the total distance (120 miles). Now we can calculate the average speed of both trips:
– 120 miles / 3 hours = 40 miles / hour.

Notice that whatever assumed distance you use, you will get the same average (go ahead and try it).



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