A bullet train leaves Kyoto for

[Vincen]

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?

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

The OA is option B.

This kind of questions like me, but I couldn't solve this one. Experts, may you give me some help? Regards.

[EconomistGMATTutor]

Hello Vincen.

Let's take a look at your question.

After the first 10 minutes, the bullet train will have traveled $$240\cdot\left(\frac{10}{60}\right)\ =\ 40\ \ \ miles.$$ Therefore, at 12:10, the distance between the bullet train and the other train is 300 - 40 = 260 miles.

The combined rate of the two trains is 240+160=400 miles per hour. Now we have to divide Distance/Rate, to find total time each will travel.

Hence, $$t=\frac{d}{v}\ \Leftrightarrow\ t=\frac{260\ m}{400\ \frac{m}{h}}=\ \frac{39h}{60}\ \\=\ \frac{39h}{60}\cdot\frac{60\min}{1\ h}=39\ \min\ \Rightarrow\ \ 39\ \text{minutes to meet each other}.$$ We have to notice that x = 39 minutes for the trains to pass each other AFTER 12:10.

Therefore the trains must have passed each other at 12:49 pm.

So, the correct answer is B.

I hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.

[Scott@TargetTestPrep]

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?

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

The OA is option B.

This kind of questions like me, but I couldn't solve this one. Experts, may you give me some help? Regards.

We can let t = the number of hours the second train has traveled when the two trains pass each other and create the equation:

240(t + 1/6) + 160t = 300

240t + 40 + 160t = 300

400t = 260

t = 260/400 = 26/40 = 13/20

Since 13/20 hour = 13/20 x 60 = 39 minutes, the trains passed each other at 12:10 pm + 39 minutes = 12:49 pm.

Answer: B