Train A leaves New York at 7:00 am traveling to Boston at

[hazelnut01]

Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?

(A)  8:15 am
(B)  8:45 am
(C)  9:00 am
(D)  9:30 am
(E)  Cannot be determined from the information given

OA=B

[GMATGuruNY]

Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?

(A)  8:15 am
(B)  8:45 am
(C)  9:00 am
(D)  9:30 am
(E)  Cannot be determined from the information given

Distance traveled by A in 3/4 hour from 7am to 7:45am = rt = (80)(3/4) = 60 miles.

Remaining distance between A and B = (total distance) - (distance travel by A) = 210-60 = 150 miles.
When A and B travel toward each other, they WORK TOGETHER to cover the 150 miles between them, so we ADD THEIR RATES.
Combined rate for A and B = 80+70 = 150mph.
At a combined rate of 150mph, the time for A and B to cover the remaining 150 miles between them = (remaining distance)/(combined rate) = 150/150 = 1 hour.

Since they start traveling toward each other at 7:45am and meet 1 hour later, the time when they pass each other = 7:45 + 1 = 8:45am.

The correct answer is B.

[Brent@GMATPrepNow]

Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?

(A)  8:15 am
(B)  8:45 am
(C)  9:00 am
(D)  9:30 am
(E)  Cannot be determined from the information given

OA=B

7:00 am to 7:45 am
During these 45 minutes (aka 0.75 hours), only train A is moving (at a speed of 80 mph)
Distance = (speed)(time) = (80)(0.75) = 60 miles
So, train A travels 60 mile
ORIGINALLY (at 7am) the two trains were 210 miles apart.
So, at 7:45 am, the trains are 150 miles apart (210 - 60 = 210)

7:45 am and on
Now BOTH trains are moving.
For every ONE hour, train A gets 80 miles closer to Boston
For every ONE hour, train B gets 70 miles closer to New York
So, for every ONE hour, the GAP between the trains decreases by 150 miles

At 7:45 am, the trains were 150 miles apart (i.e., the GAP was 150 miles)
So, after ONE HOUR, the gap will decrease from 150 miles to 0 miles (the trains will MEET)
In other words, at 8:45 am, the trains will MEET (and pass hopefully )

Answer: B

Cheers,
Brent

[[email protected]]

Hi hazelnut01,

This is an example of a Combined Rate question. These questions are typically solved with the Rate Formula and some arithmetic. For this prompt, we can also TEST THE ANSWERS.

We're given the 'start times' and rates for two trains. We're asked at what time they will pass one another.

Train A: Starts at 7am; travels 80 mph
Train B: Starts at 7:45am; travels 70 mph
Total distance between them = 210 miles

Based on these numbers, if we did some basic math, then we can figure out that at 9am Train A would have traveled 160 miles and Train B would have traveled OVER 70 miles - for a total of over 230 miles. This is clearly too much distance traveled, so the trains would have met a little before 9am. Looking at the answer choices, let's TEST Answer B...

Answer B: 8:45am

At 8:45am, Train A had traveled 1 3/4 hours at 80 mph = 140 miles
At 8:45am, Train B had traveled 1 hour at 70 mph = 70 miles
Total = 140 + 70 = 210 miles

This is an exact match for what we were told, so this must be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Jeff@TargetTestPrep]

Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?

(A)  8:15 am
(B)  8:45 am
(C)  9:00 am
(D)  9:30 am
(E)  Cannot be determined from the information given

We are given that train A is traveling at 80 mph and train B is traveling at 70 mph. Since train A leaves 45 minutes (¾ hour) before train B, we can let the time of train A = t + 3/4 and the time of train B = t.

Thus, the distance of train A is 80(t + 3/4) = 80t + 60 and the distance of train B is 70t.

Since we have a converging problem, we can use the following equation:

80t + 60 + 70t = 210

150t = 150

t = 1 hour

The trains passed each other at 7:45 + 1 hour = 8:45 a.m.

Answer: B