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rate-time problems- time differences

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rate-time problems- time differences [#permalink] New post 04 Dec 2011, 14:35
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.
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Re: rate-time problems- time differences [#permalink] New post 04 Dec 2011, 20:34
Listen to ron's rtd video-it made things very easy for me.
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Re: rate-time problems- time differences [#permalink] New post 04 Dec 2011, 21:13
sorry do you have a link? I do not know who that is. Thanks again
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Re: rate-time problems- time differences [#permalink] New post 04 Dec 2011, 21:32
Please share the link. Might help us.
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Re: rate-time problems- time differences [#permalink] New post 04 Dec 2011, 22:12
Expert's post
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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Re: rate-time problems- time differences [#permalink] New post 05 Dec 2011, 08:40
Karishma-

Thank you so much. The funny thing is, I checked my answers about 5 times last night before I made this post (not wanting to post something that was really just a stupid mistake on my part..) and guess what?! IT WAS A STUPID MISTAKE!! I guess that is what a full Sunday of studying and no sleep gets you...

Now I can rest assured knowing that my variables will be correct no matter how I assign them (as long as I do so correctly!). Thank you Karishma.
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Re: rate-time problems- time differences [#permalink] New post 06 Dec 2011, 18:29
Expert's post
On more advanced rates problems my students often falter trying to make the stimulus conform to the distance rate formula. Instead, think through the problem logically, organize the information, and then at the very end you should be able to solve using D = RT.

In this case, we have two trains traveling in opposite directions at 240 km/h and 160 km/h. (Let’s call the faster of the two Train A and the slower Train B). Therefore we should combine their rates to get 400 km/hr. Train A has already traveled for 10 minutes before the slower train begins.

Because K and T are 300 km apart, in 10 minutes train A travels 1/6 x 240 = 40 km. When train B starts the two trains are only 260 km apart. Again their combined rate is 400, so we get 260 = 400 T, T = 13/20 = 39 minutes. Because the train A already had been traveling for 10 minutes simply add that to the 39 minutes to get 49 minutes. Add that to 12:00 and you get 12:49. No complex equations or tedious number crunching.

So if you find yourself stuck on a tricky rate problem because you are trying to create a single complex equation to cough up the answer, step back from the problem, think through it, and use the simple formula D = RT.

Hope that helps! :-D
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Re: rate-time problems- time differences [#permalink] New post 06 Dec 2011, 22:49
nice explained by karishma.
Thanks karishma
Re: rate-time problems- time differences   [#permalink] 06 Dec 2011, 22:49
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