Thread: Really Basic division

Say you have to serve 500 customers within a 4 hour time frame. You know that 1 taxi can provide 1 ride an hour, hence 1 taxi can provide 4 rides in that time-frame. How many taxis would you need to serve these customers?

I know that you are supposed to do 500/4, but can someone just break this down for me? I simply don't seem to understand why you would divide. I'm confused at how you can divide 500 customers/4 rides, as the units don't fit with each other.

Thanks!

First, some basic information about division. The result of dividing m by n, by definition, answers two questions: (1) into how many groups of n elements can you divide a set of m elements and (2) if you divide a set of m elements into n equal groups, how many elements are in one group. The fact that the answers to these seemingly different questions are the same is explained by the property of multiplication that its result does not depend on the order of factors, i.e., p * n = n * p.

If we assume that one ride serves a single customer, then one taxi is able to serve 4 customers. Let's break the set of 500 people into groups of 4 according to the taxi that serves them. Then, using question (1) above, we find that there are (500 customers) / (4 customers) = 125 groups, and the number of groups equals the number of taxis.

500/4 is 125, so you have 125 customers to serve in 1 hour's time:

125 the 1st hour
125 the 2nd hour (250 so far)
125 the 3rd hour (375 so far)
125 the 4th hour (500, all done!).

now, if each taxi only holds one passenger (you really don't say), you'll need 125 taxis, one for each of the 125 customers you'll have in every hour. after one hour, the taxis (all 125 of them) will be back to pick up the 2nd hour's customers, and repeat the cycle.