While working on the following word problem, I could not solve it by making the 'time' a variable, but rather only by making the distance a variable, and I'm wondering why that is. Here is the problem:
The distance between stations A and B is 148 km. An express train left station A towards station B with the speed of 80 km/hr. At the same time, a freight train left station B towards station A with the speed of 36 km/hr. They met at station C, and by that time the express train stopped at an intermediate station for 10 min and the freight train stopped for 5 min. Find:
The distance between stations C and B.
My first attempt for a solution was to mark the time between stations A and C with the variable 'a', and similarly for variable 'b', thus:
80a = distance from A to C
36b = distance from B to C
But then I can come up with only this equation:
148 - 80a = 36b
But I can't get to the other equation needed to solve this.
However, if I mark the distance from A to C with a variable, then it becomes possible to solve it:
x = distance between B to C, thus:
(148-x)/80 +10/60 = x/36 +5/60
Why is it that I can't find a second equation when I mark the time as being unknown and then represent the distance with it?
After all, I don't know the time nor the distance...