A bullet train leaves Kyoto for

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A bullet train leaves Kyoto for

by Vincen » Tue Dec 19, 2017 7:09 am

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.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 7:09 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

Answer

by EconomistGMATTutor » Thu Dec 21, 2017 5:32 am

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.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Sep 09, 2019 6:30 pm

Vincen 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 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

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