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Trains A and B are 190 miles apart. Train A leaves one hour before tra

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Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.
[Reveal] Spoiler: OA

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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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After the first hour, A traveled 15 miles. Starting from this point, B began to travel toward A. Call x as the time for both trains meet. We have: 15x (A) + 10x (B) = 190 -15 => x =7. So, at the time both trains meet, A traveled 15 * (7+1) = 120 miles.

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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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alanforde800Maximus wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.


In one hour the distance traveled by A is 15 miles..

Thus the effective distance between A and B after 1st Hour is 175 miles (ie, 190 - 15 )

Let the distance traveled by train A be d (When they meet ), so the distance traveled by B is ( 175 - d )

Now, \(\frac{d}{15} = \frac{( 175 - d )}{10}\)

So, 10d = 2625 - 15d

Or, 25d = 2625

or, d = 105

So, Total distance travelled by train A is 120 miles ( i.e 105 + 15 )

Hence answer will be option (E)
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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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Distance b/w A and B is 190 miles

A takes a head start of 1 hr and covers 15 miles in it.

So after first hour distance b/w them is 190-15 = 175 hrs.

They will meet in time (Relative speed concept) = 175/(15+10) = 7

Total time train A travelled = 1 + 7 = 8 Hrs

Total distance covered = 15*8 = 120 miles.

Option E.

HTH

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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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alanforde800Maximus wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120


The great thing about these "multiple traveler" questions is that they can be solved in more than one way.
All we need to do is start with a word equation.
Since Train A travels for 1 hour longer than Train B, we can write:

Train A's travel time = (Train B's travel time) + 1
Let d = the distance Train A traveled
This means that 190 - d = the distance Train B traveled

Now let's transform our word equation into an algebraic equation.
Train A's travel time = (Train B's travel time) + 1
Time = distance/speed
We get: d/15 = (190 - d)/10 + 1
Multiply both sides by 30 to get: 2d = 570 - 3d + 30
Simplify: 2d = 600 - 3d
Add 3d to both sides: 5d = 600
Solve: d = 120

Answer:
[Reveal] Spoiler:
E


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Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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New post 16 Feb 2017, 20:09
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alanforde800Maximus wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120

Please assist with above problem.


Official solution from Veritas Prep.

Guiding Principles for Collision Problems

1. Make sure that the two entities are starting at the same time. If not, account for it as shown above, and reset the problem with numbers for when they are starting at the same time.

2. Add the rates of the two trains to get the total speed with which they are covering the distance. If one train is traveling at 15mph and the other at 10mph, then together they are covering 25 miles every hour.

3. Divide the distance between the two trains by their combined speed. The two trains are 175 miles apart when they start, and together they are covering 25 miles per hour, so it takes \(\frac{175}{25}\), or 7 hours, until they collide.

4. Once you have the time to collision, go back to either train to see how far they went. In 7 hours train A traveled 7hrs x 15mph, or 105 miles; train B traveled 7hrs x 10mph, or 70 miles.

5. Lastly, and on this problem most importantly, account for any distances traveled by the train that started first. Here train A traveled 15 miles before they both started and then 105 miles after, so the correct answer choice is E, 120 miles.
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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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New post 22 Feb 2017, 01:58
as we can see both the trains meet after traveling for the same time , as a started 1hr. before B then we can calculate that train A has traveled 15miles and now 175miles they both will travel so relative speed equal to 10+15=25 and they will meet after 175/25=7hrs as time is constant then a has traveled 15+7*15=120miles
so answer must be E ,
the better way to tackle time distance problems always find the constant factor such time,distance and rate .

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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra [#permalink]

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New post 05 Dec 2017, 17:37
alanforde800Maximus wrote:
Trains A and B are 190 miles apart. Train A leaves one hour before train B does, traveling at 15mph directly toward train B.Train B travels at 10mph directly toward train A. When the trains meet, how many miles has train A traveled?

a) 70
b) 85
c) 95
d) 105
e) 120


We are given that trains A and B are traveling toward each other, so we have a “converging rate problem” in which we can use the formula:

Distance traveled by train A + Distance traveled by train B = total distance

Since the two trains started 190 apart, the total distance is 190, so we have:

Distance traveled by train A + Distance traveled by train B = 190

We are given that train A travels at a rate of 15 mph and leaves one hour before train B. We are also given that train B travels at a rate of 10 mph.

We can let the time of train B = t and, since train A left one hour earlier and will have traveled for one more hour than train B, at the time they meet, the time of train A = t + 1.

Since rate x time = distance, we can calculate the distance, in terms of t, of both trains A and B.

Distance of train A = 15(t + 1) = 15t + 15

Distance of train B = 10t

Now we can substitute these values into our total distance formula and determine t.

15t + 15 + 10t = 190

25t = 175

t = 7

Thus, when the trains meet, train A has traveled (15 x 7) + 15 = 120 miles.

Answer: E
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Re: Trains A and B are 190 miles apart. Train A leaves one hour before tra   [#permalink] 05 Dec 2017, 17:37
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