Question: 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 will the trains pass each other?

1. 12:40pm
2. 12:49pm
3. 12:55pm
4. 1:00pm
5. 1:05pm

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:

Given:

• 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.
• Tokyo and Kyoto are 300 miles apart.

Find Out:

• At what time will the trains pass each other?

Train A: going from Kyoto to Tokyo
Train B: going from Tokyo to Kyoto
Let’s calculate the distance travelled by Train A by the time Train B starts at 12:10:
10 minutes at 240 mph
⅙ * 240=40miles
They have 300 – 40 = 260 miles to travel to meet each other.
Therefore, the combined rate of the two trains:
Rate(A) + Rate(B) = 400mph
By dividing Distance/Rate to find the total time each will travel:
260/400 = 39/60 >>> 39 Minutes to meet
12:10 + 39 minutes = 12:49
Therefore, the time the trains will pass each other is 12:49 pm.

Approach Solution 2:
The problem statement states that:

Given:

• 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.
• Tokyo and Kyoto are 300 miles apart.

Find Out:

• At what time will the trains pass each other?

Let distance travelled by A be x miles
Speed A = 240/60 = 4 miles per minute
Speed B = 160/60 = 8/3 miles/min
time = distance/speed
Distance travelled by A in 10 minutes = 40 miles.
Distance remaining = 260 miles.
Therefore, we can say:
3x/8 = (260-x)/4
12x = 260.8 - 8x
x = 26.4 = 104
time = 39mins
12:10 + 39 minutes = 12:49
Therefore, the time the trains will pass each other is 12:49 pm.

Approach Solution 3:
The problem statement informs that:

Given:

• 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.
• Tokyo and Kyoto are 300 miles apart.

Find Out:

• At what time will the trains pass each other?

1)Train K starts from Kyoto at 12:00 noon. It moves at the speed of 240 mph.
Let’s assume it covers 300-x miles
2)Train T starts from Tokyo at 12:10 PM at a speed of 160 mph.
Let’s assume it covers the rest of x miles
From (1) we have 300-x = 240 (t+1/6) [ we have "+1/6" here since Train K travels 10 minutes or 1/6 hours longer than train T]
and From (2) we have x = 160t
By combining the above two equations, we get:
300-160t = 240t + 40
260 = 400t
t = 26/40 = 13/20 hours = (13/20) * 60 = 39 mins.
12:10 + :39 = 12:49
Therefore, the time the trains will pass each other is 12:49 pm.

“A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The GMAT Problem Solving questions require the candidates to have basic concepts of mathematics in order to solve numerical problems. GMAT Quant practice papers help the candidates to analyse various questions that will improve their mathematical understanding.

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