Railroad Towns (Word Translation Question Bank)

[JaredT]

Is it possible to solve the following problem using a RTD chart? Thanks.

Jared


QUESTION

Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H?
(1) Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G.
(2) Train B travels at the rate of 150 miles per hour.
We are asked to find the time that it takes Train B to travel the entire distance between the two towns.

ANSWER
(1) SUFFICIENT: This tells us that B started traveling 1 hour after Train A started traveling. From the question we know that Train A had been traveling for 2 hours when the trains passed each other. Thus, train B, which started 1 hour later, must have been traveling for 2 - 1 = 1 hour when the trains passed each other.
Let’s call the point at which the two trains pass each other Point P. Train A travels from Town H to Point P in 2 hours, while Train B travels from Town G to Point P in 1 hour. Adding up these distances and times, we have it that the two trains covered the entire distance between the towns in 3 (i.e. 2 + 1) hours of combined travel time. Since both trains travel at the same rate, it will take 3 hours for either train to cover the entire distance alone. Thus, from Statement (1) we know that it will take Train B 3 hours to travel between Town G and Town H.
(2) INSUFFICIENT: This provides the rate for Train B. Since both trains travel at the same rate, this is also the rate for Train A. However, we have no information about when Train B started traveling (relative to when Train A started traveling) and we have no information about the distance between Town G and Town H. Thus, we cannot calculate any information about time.

The correct answer is A.

[StaceyKoprince]

You can use an RTD chart for any rate problem - the question is whether that's the best way to do that particular problem. In this case, I think that drawing a picture and working out the problem that way is probably going to be easier for most people.

For this, you'd set up one row for A and one row for B. But you'd have to manipulate a bit b/c this problem is weird. Most people would want to do this:

---------rate-----time----distance
A--------r---------2+y---------d
B--------r---------z---------d

But, really, by giving me info about where they cross, I could set up a chart where the distance is not equal (for each traveling the entire length between the two towns) but unequal, with each traveling some portion of the entire length such that the two portions add up to the entire length. If you call the distance between the towns d, then for the point at which they meet, one has traveled x and the other has traveled d-x.

---------rate-----time----distance
A--------r---------2---------x
B--------r---------z---------d-x

statement 1 tells me that B travels for one hour before they meet.

---------rate-----time----distance
A--------r---------2---------x
B--------r---------1---------d-x

And this is where it gets really tricky. The next thing most people are going to want to do is set up the two equations and solve - but look at your variables. Your variables are for rate and distance. They don't ask us for rate or distance. They ask us for time. And... oddly... we have real numbers in the chart already for time.

This is where you have to use logic to realize that if they meet at one spot, they have collectively covered the entire distance. If they're going the same rate (which they are), then the time it takes for them to collectively cover the distance is equal to the time it would take for one to cover the same distance by itself. So 3=3. It takes three hours for them to do it collectively and it takes three hours for one to do it individually.

This is REALLY confusing though - which is why I think it's easier to draw a line and actually plot out how everything happens.

We can use that same method to see that we don't have enough info in statement 2 - it gives me the rate but doesn't tell me anything about B's time to meet A or the overall time of either one.