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A bullet train leaves Kyoto for Tokyo traveling 240 miles

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Senior Manager
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A bullet train leaves Kyoto for Tokyo traveling 240 miles [#permalink] New post 05 Jun 2006, 10:54
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A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time wil the trains pass each other?

A. 12:40pm
B. 12:49pm
C. 12:55pm
D. 1:00pm
E. 1:05pm

I would love to know the approach you guys take to solving this. I approached it a little differently from the book. The source is MGMAT word problem translations book.
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Re: PS-Trains [#permalink] New post 05 Jun 2006, 11:13
buckkitty wrote:
A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 300 miles apart, at what time wil the trains pass each other?

A. 12:40pm
B. 12:49pm
C. 12:55pm
D. 1:00pm
E. 1:05pm

I would love to know the approach you guys take to solving this. I approached it a little differently from the book. The source is MGMAT word problem translations book.


B -

The bullet train will have travelled 240 x (10/60) miles after the first 10 minutes = 40 miles.

At 12:10 , the bullet train and the train are 260 miles apart (=300-40). To calculate when they will pass:

260 = 240*(60)*x + 160*(60)*x where x = the time it takes for them to reach one another in minutes

x = 39 minutes for the trains to pass each other AFTER 12:10.

Therefore the trains must have passed each other at 12:49
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 [#permalink] New post 05 Jun 2006, 11:20
Let distance travelled by A be x miles
Speed A = 240/60 = 4 miles per minue
Speed B = 160/60 = 8/3 miles/min
time = distance/speed
Distance travelled by A in 10 minutes = 40 miles.

Distance remaining = 260 miles.

3x/8 = (260-x)/4
12x = 260.8 - 8x
x = 26.4 = 104

time = 39mins

Hence B
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 [#permalink] New post 05 Jun 2006, 14:30
Train A: going from K to T
Train B: going from T to K

First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles

They have 300-40=260 miles to travel to meet each other.

I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph

Divide Distance/Rate to find total time each will travel:
260/400=39/60 >>> 39 Minutes to meet

12:10+39 minutes = 12:49 or Answer B
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 [#permalink] New post 05 Jun 2006, 14:36
buckkitty wrote:
Train A: going from K to T
Train B: going from T to K

First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles

They have 300-40=260 miles to travel to meet each other.

I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph

Divide Distance/Rate to find total time each will travel:
260/400=39/60 >>> 39 Minutes to meet

12:10+39 minutes = 12:49 or Answer B


Yup the combined rate approach is also a good one.
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 [#permalink] New post 06 Jun 2006, 04:52
Anyway, good job OA is B
  [#permalink] 06 Jun 2006, 04:52
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