Two trains are heading toward each other on a 750-kilometer straight track. One train is heading due east at 70 kilometers per hour and the other train is heading due west at 80 kilometers per hour. How much time do the conductors have before the trains collide?
A. 3 hours
B. 4 hours
C. 5 hours
D. 9 hours
E. 11 hours
The OA is C.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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Two trains are heading toward each other on a 750-kilometer
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EconomistGMATTutor
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Hello swerve.
Let's take a look at your question.
If we calculate the combine speed we will get 80+70= 150 km/h.
Now, the will collide in $$\frac{750km}{150\ \frac{km}{h}}=5\ h.$$ Hence, the correct answer is the option [spoiler]C=15[/spoiler].
I hope this answer can help you.
I'm available if you'd like a follow-up.
Regards.
Let's take a look at your question.
If we calculate the combine speed we will get 80+70= 150 km/h.
Now, the will collide in $$\frac{750km}{150\ \frac{km}{h}}=5\ h.$$ Hence, the correct answer is the option [spoiler]C=15[/spoiler].
I hope this answer can help you.
I'm available if you'd like a follow-up.
Regards.
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ceilidh.erickson
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Whenever 2 objects are traveling in OPPOSITE directions (toward each other or away from each other), we can always ADD their rates.
Toward:
x-----> <-----x
The SUM of their individual rates is the rate that the distance between them is CLOSING.
Away:
<----x x----->
The SUM of their individual rates is the rate that the distance between them is INCREASING.
So, these 2 trains will collectively travel the entire 750 miles to meet (crash into) each other at the sum of their individual rates, as EconomistGMAT showed.
Another strategy you can easily employ on distance problems: draw a picture!
Let's say X is the train going east, Y is the train going west:
X|------------------------------------------------|Y
0-----------------------------------------------750
After 1 hr, X has traveled 70 mi, and Y has traveled 80 mi. For Y, count backwards from 750:
|-----X------------------------------------Y-------|
0----70--------------------------------670-----750
After 2 hrs:
|---------X------------------------------Y-----------|
0-------140------------------------590----------750
After 3 hrs:
|--------------X--------------------Y----------------|
0----------210------------------510-------------750
After 4 hrs:
|----------------X------------Y------------------|
0--------------280---------430------------750
After 5 hrs:
|----------------------XY------------------------|
0---------------------350--------------------750
The answer is C.
This technique takes a bit longer, but for some people, drawing it out helps to visualize, and you're less likely to make a mistake.
Toward:
x-----> <-----x
The SUM of their individual rates is the rate that the distance between them is CLOSING.
Away:
<----x x----->
The SUM of their individual rates is the rate that the distance between them is INCREASING.
So, these 2 trains will collectively travel the entire 750 miles to meet (crash into) each other at the sum of their individual rates, as EconomistGMAT showed.
Another strategy you can easily employ on distance problems: draw a picture!
Let's say X is the train going east, Y is the train going west:
X|------------------------------------------------|Y
0-----------------------------------------------750
After 1 hr, X has traveled 70 mi, and Y has traveled 80 mi. For Y, count backwards from 750:
|-----X------------------------------------Y-------|
0----70--------------------------------670-----750
After 2 hrs:
|---------X------------------------------Y-----------|
0-------140------------------------590----------750
After 3 hrs:
|--------------X--------------------Y----------------|
0----------210------------------510-------------750
After 4 hrs:
|----------------X------------Y------------------|
0--------------280---------430------------750
After 5 hrs:
|----------------------XY------------------------|
0---------------------350--------------------750
The answer is C.
This technique takes a bit longer, but for some people, drawing it out helps to visualize, and you're less likely to make a mistake.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Jeff@TargetTestPrep
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Since the trains are heading toward each other, we can let the time when the two trains would meet be t. Since distance = rate x time, the distance of the train heading east is 70t and the distance of the train heading west is 80t.swerve wrote:Two trains are heading toward each other on a 750-kilometer straight track. One train is heading due east at 70 kilometers per hour and the other train is heading due west at 80 kilometers per hour. How much time do the conductors have before the trains collide?
A. 3 hours
B. 4 hours
C. 5 hours
D. 9 hours
E. 11 hours
Now we can determine t:
distance of 1st train + distance of 2nd train = total distance
70t + 80t = 750
150t = 750
t = 5 hours
Alternate Answer:
Since one train travels 70 km an hour and the other travels 80 km an hour, the distance between the trains decreases 70 + 80 = 150 km every hour. Since they were 750 km apart, there will be 750/150 = 5 hours for the conductors to stop them before they collide.
Answer: C
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