Suneil P. answered • 07/01/14
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Knowledgeable and Passionate University of Pennsylvania Math Tutor
Let us consider this situation more generally.
Assume there are two buses travelling toward each other head-on, and the speed of one bus is X and that of the other is Y (where these speeds are from the point of view of a stationary observer on the street); let us consider the situation from a different perspective:
From the point of view of bus going at speed X, it perceives itself as stationary while it perceives bus going speed Y as travelling toward it at speed X+Y (do you see why?)...of course, we are assuming speeds much smaller than the speed of light due to special relativity :)
Therefore, in analyzing the situation from point of view (which I will now refer to as "POV") of one of the buses, we might as well treat one bus (our POV) as stationary while the other approaches it with a speed that is the sum of the speeds of both buses (where these speeds are from the POV of bystander).
Will this affect analyses of distances/meeting times between them? NO. To illustrate, suppose we have one bus travelling 2 mph and another toward it at 3 mph and they are 5 miles apart. How long will it take for them to meet? It is not hard to see that in 1 hour they will meet (the total distance covered by them in this time would be 5 mi). If we re-conceptualize the situation by taking one bus as stationary and the other going at the sum of the two speeds (2+3 mph=5 mph), we STILL obtain that they will meet in 1 hour (even though they may meet at a different absolute location, which is irrelevant to the problem).
Therefore, with this in mind, let us pose the problem as such: call the slower bus's speed x (the faster one then is naturally going at x+8)... now try to do the problem (hint: it is the same as the above illustration except the speed is unknown rather than the time).
Hope this helps :)))