Dannyman231 wrote:
Hello all,
I can't find a consistent method for assigning variables to "time" in rate/time questions in which one participant is leaving a certain amount of time before or after the other.
Why do I get different answers when I assign participant A's time variable as "t" and participant B's as "t+1" (for example), as opposed to participant A's as "t-1" and participant B's as "t"?? (assuming of course, that I am consistent).
Considering this example:
Train A leaves Kyoto to Tokyo traveling at 240mph at 12noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160mph. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?
I understand that I need to setup time variable for both trains, multiply them by their respective rates, add them together and set them against 300 miles (the trains are meeting each other), but I get different answers when I set train A's time as "t" and B's as "t-1/6" as to when I seIst train A's time as "t+1/6" and train B's as "t"... why? Does this only happen in "kiss" problems, where two participants are meeting each other from two different points?
Is there a consistent method to employ in these instances? Thanks in advance.
There is no reason why you should not get the same answer in both the cases. It doesn't matter whom you assign t. Just make sure that once you get the value of t, you think back and decide whether the answer required is t or something else. Here are the two cases:
Train A leaves Kyoto to Tokyo traveling at 240mph at 12noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160mph. If Tokyo and Kyoto are 300 miles apart, at what time will the trains pass each other?
Train A leaves at 12 noon and train B leaves at 12:10.
Case 1:
Let's say A travels for t hrs. Then, B travels for (t - 1/6) hrs
240*t + 160*(t - 1/6) = 300
400t = 980/3
t = 98/120 hrs = 49 minutes
Train A meets train B 49 minutes after it starts i.e. at 12:49 pm
Case 2:
Let's say B travels for t hrs. Then, A travels for (t+1/6) hrs
240*(t + 1/6) + 160*t = 300
400t = 260
t = 13/20 hrs = 39 minutes
Train B meets train A 39 minutes after it starts i.e. 39 minutes past 12:10 i.e. 12:49
You do get different values for t but that is expected since t stands for different periods of time in the two cases. But in either case, they meet at the same time (again which is expected since how you assign your variables doesn't affect your answer)
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