maris said:
I may be under the wrong topic, so if I am please forgive me and direct me to the correct one if you do not mind.
My problem:
If a bridge crosses over a river that is 1520 ft wide and one bank of the river holds 1/5 of the bridge and the other holds 1/6 of the bridge how long is the bridge?
My first instinct was to take 1/5 of 1520 and then 1/6 of 1520, add them and then subtract the total from 1520, but I stopped as I realized this isn't the way to do it. I am blocked, and I know it must be simpler than I am making it.
Any suggestions? (See below)
Thanks very much for your patience and assistance.
Maris
mmm's advice above is very good.
In general, it is an excellent method for almost all "word problems" to translate the problem into mathematical language before doing anything else. That is because mathematical language has been designed over centuries to facilitate logical thought about things like numbers, space, and time.
Almost always, the first step is to "name things mathematically," which means to assign a unique symbol to each concept that the problem concerns. Note that the first thing mmm did was say x = length of bridge. Obviously the choice of x rather than L or b is purely arbitrary. The point is that the concept "length of bridge" is now captued in a symbol that can be manipulated easily in mathematics.
The second step is to write down USING YOUR CHOSEN SYMBOLS and numbers all the information ALREADY GIVEN in the problem. See how mmm did it.
part of bridge over water = 1520
part of bridge over one bank = (1/5)x
part of bridge over other bank = (1/6)x.
The third step is to form one or more equations relevant to your problem USING YOUR SYMBOLS and the GIVENS. All the other steps in solving the problem are mechanical, but setting up the equation for a new kind of problem may take some creativity. In this case, mmm gave you a hint.
The last step is to solve your equation. At this point, it is no longer a word problem; you just apply mechanically the rules of algebra or calculus or whatever to solving your equation.
If you learn to follow this procedure, "word problems" will lose their terror. At least when I was being taught math, no one told me this procedure (or if they did I was daydreaming that day). So I thought it worthwhile to generalize on mmm's answer in case you too had never been given a general technique for solving word problems. If you can find in a library Polya's book "How To Solve It," I advise reading it.