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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, 12:44
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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 Source: GMAT Prep Now  http://www.gmatprepnow.com/module/gmat ... /video/914
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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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15 Sep 2015, 12:52
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?



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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15 Sep 2015, 13:55
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
Ans= B



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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, 13:57
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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 = 2A 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.



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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15 Sep 2015, 14:12
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 = 2A 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. Shoot! Nice catch. Thanks



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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16 Sep 2015, 00:36
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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.



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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16 Sep 2015, 08:07
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?



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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16 Sep 2015, 22:34
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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)



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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17 Sep 2015, 09:06
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



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Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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17 Sep 2015, 16:00
let t=time to work time to home (derived from inverse kmh ratio)=75t/105➡5t/7 t+5t/7=2 hours total time t=7/6 hours➡70 minutes



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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18 Sep 2015, 21:25
[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.



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Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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30 Jun 2016, 10:53
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
Roundtrip average speed: (2*75*105)/(75+105)=525/6 Roundtrip time=2 hrs given So roundtrip distance=(526/6)*2=175 kms Singletrip distance=175/2 kms...Time taken to cover this distance at 75kmph= (175/2)/75 hrs=70 mins.



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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03 Oct 2017, 00:55
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



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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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03 Oct 2017, 04:22
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.
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Re: Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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05 Oct 2017, 09:12
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 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
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Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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05 Oct 2017, 16:19
Thanks
Last edited by Buttercup3 on 11 Feb 2018, 19:29, edited 1 time in total.



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Cole drove from home to work at an average speed of 75 kmh. He then [#permalink]
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05 Oct 2017, 18:03
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 Source: GMAT Prep Now  http://www.gmatprepnow.com/module/gmat ... /video/914I avoid division if I can in RTD problems. I solved for time with multiplication. It's fast. Total time = 2 hours Let time from home to work = x So time from work to home = (2x) Rate, home to work = 75 kmh Rate, work to home = 105 kmh \(r*t=D\)D, home to work: (75*x) D, work to home: (105)*(2x) \(D\) is equal both ways, hence \(75x = (105)(2x)\) \(75x = 210  105x\) \(180x = 210\) \(x = \frac{210}{180} = \frac{21}{18} =\frac{7}{6}hrs\) Any fraction of an hour can be multiplied by 60 to obtain minutes. \(x =\frac{7}{6}hrs * 60\) = 70 minutes Answer B
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