The Z train leaves station A moving at a constant speed, and passes by

Question

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

A. 1.8m
B. 6m
C. 7m
D. 9m
E. 12m

chetan2u · Answer

A very easy way would be to look at it logically.

Stations......distance......time
A to B ..........x+m..........7hrs
B to C ............x.............5hrs

So the excess (x+m)-x or m kms is covered in 7-5 or 2 hrs. 
Thus the train travels m km in 2 hrs.

But the total time taken from A to C is 5+7 or 12 hrs. 
So, the train will travel 12*m/2 or 6m in 12 hrs.

B

darkprince2901 · Answer

A_________x+m_________B____x____C

Given, speed is constant 
S= D/T

(x+m)/7 = x/5
on solving => x=5m/2

Distance from A to C -> x+m + x
AC = 5m/2 +5m/2 +m = 6m -> B

Shilpabansal89 · Answer

One more solution to this can be :
Speed between A to B and between B to C will remain constant. Therefore, x+m/7 = x/5
from which x=2.5m
Now, distance between A to C is 2x+m. Putting the value of x=2.5m we get distance between A to C = 6m

Ratisbon1993 · Answer

Let distance between B and C = d
Let distance between A and B = d + m
t to get from B to C =5
t to get from A to B = 7

What we're solving for is the total distance between A and B, so --> 2d + m

The key here is that the train is  moving at constant speed , so we can equate the rates from A to B and from B to C:
r = d/t

(d+m)/7 = d/5

5d + 5m = 7d (after cross-multiplication)

2d = 5m

d = 5m/2

Now, that we know the relationship between d and m, we can express the total distance 2d + m in terms of m.

2(5m/2)+m = 6m

Answer: B

hykhan · Answer

A quick way to solve this question is to plug an easy number for speed.

Say the train is travelling at 100mph. In 7 hours it’s travelled 700km from A to B. Then in another 5 hours it’s travelled another 500km.

700 = 500 + m
m therefore equals 200

The distance from A to C is thus 700+500=1200

In terms of m (200), the distance from A to C is 1200/200 = 6m

B is your answer

Posted from my mobile device

effatara · Answer

Let the speed of the train be 's' kph. Then: 
AB=7s and BC=5s and AC=12s
7s=5s+m...> m=2s
AC=12s=6*2s=6m

ANS:B

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The Z train leaves station A moving at a constant speed, and passes by

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