GMAT QUANT QUESTION - Rates

We can and we do. It is called the concept of relative speed.

We add two rates when two objects/people work together to complete a work.

Using the same logic, when two objects move toward each other to "work" simultaneously (which means reduce the distance between them by travelling toward each other) we add their individual speeds. What we get is the relative speed. It is the speed at which the distance between the objects reduces.

The “work rate” is defined as the fraction of the work completed in a certain amount of time. For instance, if it takes 3 days for a worker to complete the job, the rate is 1/3 job/day. If you have the rates of two workers with the same unit of time, you can add the rates. For instance, if two workers complete a job in 3 and 5 days; their rates are 1/3 and 1/5 and the combined rate is 1/3 + 1/5. The idea here is the following: In one day, 1/3 of the job is completed by one worker and 1/5 is completed by the other; thus, in total, 1/3 + 1/5 = 8/15 of the job is completed.

For average speeds, we can’t simply add the average speeds belonging to two different parts of the journey to find the average speed of the whole journey. If a car travels a part of a trip at an average speed of 35 mph and the rest at 55 mph, it does not make sense for the whole trip to have an average speed of 35 + 55 = 80 mph. Without knowing anything else, we can only be sure that the average speed for the whole journey will be something between 35 and 55.