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Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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15 Sep 2015, 13:44

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Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

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15 Sep 2015, 13:52

I tried solving the question by starting with this: time to work + time home = 2 d/75 + d/105 = 2 105d/7875 + 75d/7875 = 15750 180d/7875 = 15750 180d = 7875*15750 I used my calculator for the rest and got d = 689062.5 which is obviously too big to work with the question. So I stopped. What went wrong?

Concentration: International Business, General Management

GMAT 1: 660 Q49 V32

WE: Business Development (Energy and Utilities)

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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15 Sep 2015, 14:55

Let the distance one way be x Time from home to work = x/75 Time from work to home = x/105 Total time = 2 hrs (x/75) + (x/105)= 2 Solving for x, we get x = 175/2

Time from home to work in minutes= (175/2)*60/75 = 70 minutes

Concentration: International Business, General Management

GMAT 1: 660 Q49 V32

WE: Business Development (Energy and Utilities)

Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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15 Sep 2015, 14:57

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skylimit wrote:

I tried solving the question by starting with this: time to work + time home = 2 d/75 + d/105 = 2 105d/7875 + 75d/7875 = 15750 180d/7875 = 15750 180d = 7875*15750 I used my calculator for the rest and got d = 689062.5 which is obviously too big to work with the question. So I stopped. What went wrong?

The error lies in your 2nd step- 105d/7875 + 75d/7875 = 15750

It should be 105d/7875 + 75d/7875 = 2

A better approach would be to take the common factors out. This way the calculation becomes much simpler. In this case taking common factor "15" out we get:

(1/15)*[(d/5)+(d/7)]= 2 --> (d/5)+(d/7)=30; which is much easier to solve manually. Remember, if you think you need a calculator on any GMAT question then probably your approach is not correct. There is always a way around.

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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15 Sep 2015, 15:12

sunnysid wrote:

skylimit wrote:

I tried solving the question by starting with this: time to work + time home = 2 d/75 + d/105 = 2 105d/7875 + 75d/7875 = 15750 180d/7875 = 15750 180d = 7875*15750 I used my calculator for the rest and got d = 689062.5 which is obviously too big to work with the question. So I stopped. What went wrong?

The error lies in your 2nd step- 105d/7875 + 75d/7875 = 15750

It should be 105d/7875 + 75d/7875 = 2

A better approach would be to take the common factors out. This way the calculation becomes much simpler. In this case taking common factor "15" out we get:

(1/15)*[(d/5)+(d/7)]= 2 --> (d/5)+(d/7)=30; which is much easier to solve manually. Remember, if you think you need a calculator on any GMAT question then probably your approach is not correct. There is always a way around.

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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16 Sep 2015, 01:36

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[quote="skylimit"]Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

Hi All,

Here is my first post...

I prefer to use the ratio approach when it is possible, in this case it is.

The ratios between the speeds Work:Home = 75:105 = 5:7 Given that the distance in both directions is the same, the ratios of times becomes Work:Home = 7:5 (inverse)

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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16 Sep 2015, 09:07

zurvy wrote:

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

The inverse method is interesting and it seems pretty fast too. I just don't understand the very last part above. Why did you multiply 2/12 by 7 and then multiply by 5 to get minutes?

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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16 Sep 2015, 23:34

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skylimit wrote:

zurvy wrote:

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

The inverse method is interesting and it seems pretty fast too. I just don't understand the very last part above. Why did you multiply 2/12 by 7 and then multiply by 5 to get minutes?

Hi there,

The ratio of time is as explained 5:7 during the entire trip , and it took a total of 2 hours ==> Imagine it like this, you have to split the 2 hours with a ratio of 5:7 ==> The total parts would be in this case 5+7 = 12 ==> so The total time has to be divided first by 12, and then multiplied by 5. If I told you to split 24 apples among two persons with a ratio of 5:7, you would first divide 24/12 (12=7+5) and than multiple by 5 and 7 respectively to get the answer. 24/12 * 5 = 10 for one person 24/12 * 7 = 14 for the other making a total of 24 apples.

Regarding the multiplication by 5, you need to convert 14/12 to fractions of 60 (so you get the minutes). (5*14/5*12 = 70/60) Or you could, 14/12 = 7/6 hour = 1 1/6 hour = 1 hour and 10 minutes = 70/60 hour (its just playing with fractions, and with time, having a denominator of 60, always gives you the number of minutes at the top)

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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17 Sep 2015, 10:06

zurvy wrote:

skylimit wrote:

zurvy wrote:

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

The inverse method is interesting and it seems pretty fast too. I just don't understand the very last part above. Why did you multiply 2/12 by 7 and then multiply by 5 to get minutes?

Hi there,

The ratio of time is as explained 5:7 during the entire trip , and it took a total of 2 hours ==> Imagine it like this, you have to split the 2 hours with a ratio of 5:7 ==> The total parts would be in this case 5+7 = 12 ==> so The total time has to be divided first by 12, and then multiplied by 5. If I told you to split 24 apples among two persons with a ratio of 5:7, you would first divide 24/12 (12=7+5) and than multiple by 5 and 7 respectively to get the answer. 24/12 * 5 = 10 for one person 24/12 * 7 = 14 for the other making a total of 24 apples.

Regarding the multiplication by 5, you need to convert 14/12 to fractions of 60 (so you get the minutes). (5*14/5*12 = 70/60) Or you could, 14/12 = 7/6 hour = 1 1/6 hour = 1 hour and 10 minutes = 70/60 hour (its just playing with fractions, and with time, having a denominator of 60, always gives you the number of minutes at the top)

Thanks zurvy! I didn't realize you multiplied by 5 to get a denominator of 60. Nice solution

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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18 Sep 2015, 22:25

[quote="skylimit"]Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

Answer : B

First round distance travelled (say) = d Speed = 75 k/h Time taken, T2 = d/75 hr

Second round distance traveled = d (same distance) Speed = 105 k/h Time taken, T2 = d/105 hr

Total time taken = 2 hrs Therefore , 2 = d/75 + d/105 LCM of 75 and 105 = 525

2= d/75 + d/105 => 2 = 7d/525 + 5d/525 => d = 525 / 6 Km

Therefore, T1= d/75 => T1 = 525 / (6 x 75) => T1 = (7 x 60) / 6 -- in minutes => T1 = 70 minutes.

Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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30 Jun 2016, 11:53

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

Round-trip average speed: (2*75*105)/(75+105)=525/6 Round-trip time=2 hrs given So round-trip distance=(526/6)*2=175 kms Single-trip distance=175/2 kms...Time taken to cover this distance at 75kmph= (175/2)/75 hrs=70 mins.

Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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03 Oct 2017, 05:22

santro789 wrote:

Time = distance /speed

So Lets consider D =100

Therefore , 100/75(60) +100/105(50)= 120 mins

Is the right way of thinking ?

Can someone please explain this with logic not formulas

It is incorrect to assume the value of distance D as we have a constrain on time ( t1+t2 = 2 hours ).

We know the avg speed for first half is 75kmph => D = 75 * T1 We also know the avg speed for second half is 105kmph => D = 105*T2

Since the distance is same we can equate the above equations 75*T1 = 105*T2 => 5T1=7T2. Now we know the total time taken is 2 hours => T1+T2 = 2 On solving we will get T1 = 7/6 hours which is 70 minutes.
_________________

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

We use the formula distance = rate x time, or equivalently, time = distance/rate. We can let the distance either way = d; thus, Cole’s time from home to work is d/75 and his time from work to home is d/105. The total travel time is given as 2 hours, so we have:

d/75 + d/105 = 2

Multiplying the entire equation by 525, we have:

7d + 5d = 1050

12d = 1050

d = 1050/12 = 525/6 = 175/2 km

Thus, it took him (175/2)/75 = 175/150 = 7/6 hours = 7/6 x 60 = 70 minutes.

Answer: B
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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05 Oct 2017, 17:19

zurvy wrote:

skylimit wrote:

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78

Hi All,

Here is my first post...

I prefer to use the ratio approach when it is possible, in this case it is.

The ratios between the speeds Work:Home = 75:105 = 5:7 Given that the distance in both directions is the same, the ratios of times becomes Work:Home = 7:5 (inverse)

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

Very good explanation though. But I did not understand the purpose of taking the inverse of the ratio from 5:7 Don't we have to calculate time taken from home to work? TIA

Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]

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05 Oct 2017, 19:03

skylimit wrote:

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work? A) 66 B) 70 C) 72 D) 75 E) 78