Average speed in GRE Quant

The average speed of an object is defined as the total distance traveled by the object divided by the total time taken to cover that distance. Average speed is a scalar quantity, which means it is defined only by the magnitude and not by the direction. Students often commit the mistake of averaging two speeds together to get the average speed. Averaging the two speeds will give you the right answer only when a person travels at each value of speed for an equal amount of time. Let’s have a look at a few examples to develop a better understanding of this concept:

1. Derek drives 100 km at 50 km/h, and then he drives the next 90 km at 30 km/h. What is his average speed for the entire trip in kilometer per hour?

  1. 30
  2. 38
  3. 40
  4. 45
  5. 52

Most students will simply take the average of two speeds, which will not give them the right answer:

(50 km/h + 30 km/h)/2 = 40 km/h

40 km/h might seem like the right answer, but it’s not!

The right way to calculate the average speed is to divide total distance by total time. It can be represented in the form of a mathematical formula as:

Average speed = Total distance/ Total time

Let’s use this formula to get the right answer, by dividing the equation into two parts:

Firstly, we have to calculate the total distance traveled by Derek, which is equal to 100 km + 90 km = 190 km

Secondly, we must calculate the total time taken by Derek to complete his journey.

  • The time taken by Derek to travel the first 100 km at the speed of 50 km/h is equal to (100/2) = 2 hours
  • The time taken by Derek to travel the next 90 km at the speed of 30 km/h is equal to (90/30) = 3 hours

So, the total time taken by Derek to complete the entire journey = (2+3) = 5 hours

On putting these two values in the formula mentioned above, we will get the correct value of average speed.

Average speed = Total distance/Total time = 190/5 = 38 km/h

Now, let’s try to solve a slightly more complicated problem.

2. Shania drives from point A to B at 100 km/h then triples her speed and travels from point B to C. If the distance from point B to C is double the distance from point A to B, then what is Shania’s average speed?

  1. 200
  2. 175
  3. 180
  4. 195
  5. 220

Let the distance between points A and B is equal to x. So, the distance from point B to C becomes 2x and the total distance from point A to C becomes 3x.

Now, we must calculate the total time taken by Shania to drive from point A to C.

Time taken by Shania to travel from point A to point B is x/100

Time taken by Shania to travel from point B to point C is 2x/300

Therefore, the total time taken to travel from point A to C = x/100 + 2x/300 = 5x/300

Since we already know the formula to calculate average speed = (Total Distance/ Total Time)

On putting the two values in the formula, we get:

Average speed = 3x/(5x/300) = 180 km/h

Developing a good understanding of the concept always helps in increasing accuracy while solving the questions. Use this simple formula to solve more questions related to the concept of average speed. BYJU’S will be glad to help you in yourGRE preparation journey. You can ask for any assistance related to GRE from us by just giving a missed call at +918884544444, or you can drop an SMS. You can write to us at gre@byjus.com.