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Carl drove from his home to the beach at an average speed of [#permalink]
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16 Nov 2003, 17:20
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Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers did Carl drive each way? (A) 350 (B) 345 (C) 320 (D) 280 (E) 240
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Last edited by Bunuel on 11 Apr 2014, 02:59, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.



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Distance will be the same... so, D1 = D2
80*t = 70*(t+1/2)
gives t=7/2
distance=80*7/2 = 280



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Yep, agree on D. I'd also agree with dj's explanation. That is a very simple and short way of doing this. The key is recognizing how to set up the equation.



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See if the following helps
I think you can solve such problems in lesser time, if you always follow one approach consistently. You can always solve any such problem by using the Distance formula. The moment you see distances/times or speeds put down the formula and try to fit in given information.
Distance= Speed * Time.
Distance  Is being asked so don't know  D
Speed  Given 80
Time  don't know so T.
D= 80*T
Wait.. speed is given twice. So put down the equation again.
Distance  D2
Speed  70
Time  don't know so T2
D2 = 70 * T2
What all information do we have ?
1) The distance is the same. So D=D2
2) The time taken to return is 1/2 hr more than the time taken to go to the beach => T + 1/2 = T2
Therefore D=80*T = 70*(T+1/2) => T= 3.5 => D= 80*3.5= 280. D is the answer.
Usually we take more time to solve when we don't get an exact sense of the question or if we are torn between two ore more methods to solve. This usually happens if you can sense the possibility of easy solution but are not quite clear about what it is.
Probably the intuitive method would be > In half an hour at 70 km/hr Carl would have travelled 35 k.m. At a difference in speed of 10 km/hr how much time would it take to fall behind by 35 km? 35/10 = 3.5 hrs. So the distance travelled in these 3.5 hrs = 3.5 * 80
(Think of somebody else starting from the other side at the same time (and the speed of 10km/hr) Carl starts his return. In the time Carl would take to go to the beach, our guy will meet Carl and would have travelled 35 km. Therefore, the time taken by him =35/10 which will also be equal to the time taken by Carl to go to the beach.)
But it's difficult to rely on being able to use such intuitive approaches during the test. Such approaches tend to be problem specific and if you are under pressure, you may find it difficult to think clearly enough to get such solutions. I think it would be better to go to the test with some straight forward methods for such straight questions and leave the intuitive thinking for the really tough questions where you may not have the easier alternative.
Or, you can solve few speed/distance problems before the test. This usually helps.



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pawargmat
Considering how much time I waste on problems like these, I think your advice is probably very good.
Any other suggestions?



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pawargmat....thank you for that explanation...i think that's just what i needed....



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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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08 Apr 2014, 20:47
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[quote="guy123"]Carl drove from his home to the beach at an average speed of 80 km/hr and returned home by the same route at an average speed of 70km/hr. If the trip home took 1/2 hour longer than the trip to the beach, how many km did Carl drive each way? A)350 B)345 C)320 D)280 E)240 Let us backsolve here. The answer option has to be divisible by 7 to give us 1/2. Let us try 280 km. Time taken will be 3.5 hours and 4 hours. Hence D is the answer.
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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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10 Apr 2014, 23:51
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guy123 wrote: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took hour longer than the trip to the beach, how many kilometers did Carl drive each way?
(A) 350 (B) 345 (C) 320 (D) 280 (E) 240 Is it half hour longer or hour longer?



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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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11 Apr 2014, 00:02
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ind23 wrote: guy123 wrote: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took hour longer than the trip to the beach, how many kilometers did Carl drive each way?
(A) 350 (B) 345 (C) 320 (D) 280 (E) 240 Is it half hour longer or hour longer? Can someone please edit the question? It should be 1/2 hr; 1 hr gives the answer = 560
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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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11 Apr 2014, 03:00



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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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20 Apr 2014, 20:57
D/70D/80=1/2 D=280



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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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23 Oct 2014, 01:27
Distances are same. Let d be the time taken to beach . So distance to beach be 80t . Distance to home will be 70(t+0.5) . Equating both distances, 80t=70t+70(0.5) t=3.5 substituting the value in 80t, we get the distance as 280
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Re: Carl drove from his home to the beach at an average speed of [#permalink]
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