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The Z train leaves station A moving at a constant speed, and [#permalink]
30 Oct 2012, 20:45
1
This post received KUDOS
3
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
35% (medium)
Question Stats:
76% (02:53) correct
24% (02:49) wrong based on 161 sessions
The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
A. 1.8m B. 6m C. 7m D. 9m E. 12m
This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here.
Correct. According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows. Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km.
Re: The Z train leaves station A moving at a constant speed, and [#permalink]
30 Oct 2012, 20:57
4
This post received KUDOS
anon1 wrote:
The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
1.8m 6m 7m 9m 12m
This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here.
Correct. According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows. Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km.
The reason it is failing for you is that you chose incorrect numbers. If the question says it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem. AB = 7, BC=5 Therefore AB-BC = 2
But from question, AB-BC =m => m=2
Now total distance = AB+BC= 12 Substitute 12 to get answer in terms of m Total distance =12 =6m
Ans B
So you get right answer not by plugging in numbers but by 'plugging in right numbers'
Hope it helps and if does, kudos is right there << _________________
Re: The Z train leaves station A moving at a constant speed, and [#permalink]
23 Feb 2013, 07:03
2
This post received KUDOS
Time taken from A to B = 7 hours
Time taken from B to C = 5 hours
Distance from A to B is \(m\) miles more than distance between B to C. Since the average speed is constant, time taken to travel \(m\) miles is 7-5 = 2 hours.
Total time taken for the entire trip (A to C) = 7 + 5 = 12hours
in 12 hours you can travel \(\frac{12}{2}*m\) miles = 6m miles.
Re: The Z train leaves station A moving at a constant speed, and [#permalink]
29 Mar 2013, 02:33
4
This post received KUDOS
Expert's post
anon1 wrote:
The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
A. 1.8m B. 6m C. 7m D. 9m E. 12m
This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here.
Correct. According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows. Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km.
Use a variable, plug in numbers or simply look at the big picture:
A to B the distance is m km extra and the train takes 2 hrs extra to cover m kms. Then, what is the speed of the train? It is (m/2) kms/hr So the distance between A and C = Speed* Time = (m/2)*12 = 6m _________________
Re: The Z train leaves station A moving at a constant speed, and [#permalink]
26 Nov 2013, 09:12
1
This post received KUDOS
anon1 wrote:
The Z train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Z train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
A. 1.8m B. 6m C. 7m D. 9m E. 12m
This question was difficult for me. I actually did the problem exactly the way the "alternative method" suggests but did not find an answer that worked. I picked m=7. my distance from b to c was 3. Therefore my distance from a to b was 10. So the total distance from a to c is 13. My goal is 13, with an m of 7. B does not fit this.... why does this not work? It seems like plugging in is failing me here.
Correct. According to this answer, the distance between A and C is 6m. If the distance between A and C is 6m, using our plug in of m=3 the distance is 18. Equate 2s+3 (the distance between A and C according to our table) with 18:
2s+3=6m=18
--> 2s=18-3=15 /:2
--> s=7.5
Use s=7.5 to calculate v, by applying the Distance = Speed×Time formula on the second row:
v∙5=7.5 \:5
---> v=1.5
check if v=1.5 fits the first row:
1.5∙7= 7.5+3= 10.5
7∙1.5 is indeed 10.5, so 6m makes for a velocity that fits both rows. Therefore, this answer choice is correct.
Alternative method:
Plug in a number for the distance and find the resulting m, rather than the other way around.
For example, plug in a distance of 12 km A-C. Since the speed is constant, divide the distances of A-B and B-C as 7 km and 5 km, respectively, making m equal 7-5=2 additional kilometers in the first leg. The question asks for the value of the distance A-C, which we denoted as 12 km, and the m we plug in is m=2: only answer B will match your goal of 12 km.
Let's say 'r' is the constant rate Then we have Distance from A to B = 7r Also distance from B to C = 5r
The difference between the distanced 7r - 5r = m 2r = m
Total distance is 12r (7r+5r) So in terms of m---> 12 (1/2) = 6m
Re: The Z train leaves station A moving at a constant speed, and [#permalink]
07 Dec 2015, 02:20
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