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# Tom and John traveled in the same direction along the equal route at

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Math Revolution GMAT Instructor
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Tom and John traveled in the same direction along the equal route at [#permalink]

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14 May 2016, 01:59
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Difficulty:

45% (medium)

Question Stats:

74% (02:02) correct 26% (02:08) wrong based on 160 sessions

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Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min
B. 6 min
C. 7 and 1/2 min
D. 8 min
E. 10 min

* The answer will be posted in two days.
[Reveal] Spoiler: OA

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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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14 May 2016, 09:14
Relative speed = 10 - 5 = 5

Distance traveled in 15 mins or 1/4 hrs = 5/4 kms

John travels 10 kms in 1 hour
John travels 5/4 kms in 5/(4*10) = 1/8 hrs = 7.5 mins

Math Expert
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Posts: 5662
Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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14 May 2016, 09:19
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MathRevolution wrote:
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min
B. 6 min
C. 7 and 1/2 min
D. 8 min
E. 10 min

* The answer will be posted in two days.

Firstly the Q should be " how many MORE minutes it takes John to reach the station?"

TOM's speed = 15kmph, ........... JOHN's speed = 10KMPH....
so in 15 minutes, tom takes a lead of $$\frac{(15-10)}{60} *15 = \frac{5}{60}* 15 = \frac{5}{4}km$$..
John has to cover this$$\frac{5}{4}$$ km..
With speed of 10kmph, he will cover this distance in $$\frac{5}{4}*\frac{60}{10}= \frac{15}{2} = 7 and \frac{1}{2}..min$$
C
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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16 May 2016, 18:56
Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence, 6(5/4)=15/2 minutes. The correct answer is C.
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Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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22 Feb 2017, 17:16
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Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min
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Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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22 Feb 2017, 18:27
AustinKL wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

since passing John, Tom has gone 10 min*1/3 kpm=10/3 k
in the same ten minutes, John has gone 10 min*1/5 kpm=2 k
John needs 10/3-2=4/3 k more to reach gas station
(4/3 k)/(1/5 kpm)=6 2/3 min for John to reach gas station
C
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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20 Mar 2017, 08:09
chetan2u wrote:

Firstly the Q should be " how many MORE minutes it takes John to reach the station?"

That makes such a huge difference!!! I was not able to solve this problem because the question was not worded correctly
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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20 Mar 2017, 13:31
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Math Revolution, if you want people to buy your product, you should ensure the prompts use clear and concise English.
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Re: Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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10 May 2017, 23:27
gracie wrote:
AustinKL wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

since passing John, Tom has gone 10 min*1/3 kpm=10/3 k
in the same ten minutes, John has gone 10 min*1/5 kpm=2 k
John needs 10/3-2=4/3 k more to reach gas station
(4/3 k)/(1/5 kpm)=6 2/3 min for John to reach gas station
C

if both are travelling in same direction...then it means as per question john was 10 mins ahead of TOM...so as relative speed of 8kmph it took 4/3 km more distance that tom had to cover and john covered only 2km as (12 kmph for 10mins)...so john travelled 2km to reach gas station....so it took him 10 mins
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Re: Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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11 May 2017, 01:08
ziyuen wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

$$20km/h = \frac{20km}{1h}=\frac{20km}{60min}=\frac{1km}{3min}=\frac{1}{3}km/min$$
$$12km/h = \frac{12km}{1h}=\frac{12km}{60min}=\frac{1km}{5min}=\frac{1}{5}km/min$$

It took Tom 10 mins to travel to Gas station. The distance is: $$\frac{1}{3} \times 10 = \frac{10}{3} km$$

To reach gas station, John needs to travel in: $$\frac{10}{3}:\frac{1}{5}=\frac{50}{3}=16\frac{2}{3} min$$ after Tom passes John.

Hence, since Tom reached gas station, John needs to travel $$16\frac{2}{3}-10=6\frac{2}{3} min$$ to reach gas station.

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Re: Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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15 May 2017, 16:29
ziyuen wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

We are given that Tom rides at 20 km per hour and John rides at 12 km per hour.

If Tom reaches a gas station in 10 minutes, or 1/6 hour, after passing John, then he has ridden 20 x 1/6 = 10/3 kilometers.

Since time = distance/rate, it will take John (10/3)/12 = 10/36 = 5/18 hour to reach the gas station.

5/18 hour is 5/18 x 60 = 50/3 = 16 2/3 minutes.

Thus, John arrives at the gas station 16 2/3 - 10 = 6 2/3 minutes after Tom reaches it.

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Re: Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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20 May 2017, 01:44
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hazelnut wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

Please write correct English when posting questions. The question is very easy but very badly worded. Please correct it.

Posted from my mobile device
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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06 Sep 2017, 04:25
MathRevolution wrote:
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min
B. 6 min
C. 7 and 1/2 min
D. 8 min
E. 10 min

* The answer will be posted in two days.

Using relative speed , the distance travelled = 15*5/60 = 5/4 km.

Time taken for J = 5/4*1/10 hr= 1/8 hrs = 7.5 mins.

Ans:C
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Re: Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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06 Sep 2017, 04:39
hazelnut wrote:
Tom and John both ride a bicycle in the same direction on an equal route at their constant speed rates of 20 km per hour and 12 km per hour, respectively. After 10 minutes Tom passes John, he reaches a gas station. How many minutes does it take John to reach the gas station?

A. 5 min

B. 6 min

C. 6 and $$\frac{2}{3}$$ min

D. 10 min

E. 15 min

Using relative speed distance= 10 mins* 8km/60 = 4/3 kms.

Now John needs = 4/3* 60/12= 20 /3 mins

Ans:C
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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11 Sep 2017, 09:55
MathRevolution wrote:
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min
B. 6 min
C. 7 and 1/2 min
D. 8 min
E. 10 min

In 15 minutes, or 1/4 hour, Tom travels 15 x 1/4 = 15/4 km and John travels 10 x 1/4 = 10/4 km. Thus, John has to travel 15/4 - 10/4 = 5/4 km to catch up to Tom.

Therefore, it takes John (5/4)/10 = 5/40 = 1/8 hours, or 7.5 minutes, to catch up to Tom.

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Tom and John both ride a bicycle in the same direction on an equal rou [#permalink]

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12 Sep 2017, 07:41
Tom gains 8 km/h on John, or (4/3)km per 10 minutes. Now we have to find out in how many minutes is John able to cover that distance.

Since average speed = distance/time:

$$Time = (4/3)/12 = (1/9) hours$$

(1/9) hours * 60 minutes = (20/3) minutes -> 6 minutes and 40 seconds, or 6 minutes and (2/3) minutes.
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Re: Tom and John traveled in the same direction along the equal route at [#permalink]

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01 Oct 2017, 07:22
i felt the question is not a gmat level question as it is not having correct explanation of the time asked for starts from when.

same question given with different data set in following link... with different difficulty level.
https://gmatclub.com/forum/tom-and-john ... 34625.html

MathRevolution wrote:
Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many minutes it takes John to reach the station?
A. 5 min
B. 6 min
C. 7 and 1/2 min
D. 8 min
E. 10 min

* The answer will be posted in two days.
Re: Tom and John traveled in the same direction along the equal route at   [#permalink] 01 Oct 2017, 07:22
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