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24 Aug 2013, 22:54
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B
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Difficulty:
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Question Stats:
79% (02:46) correct
21%
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A start walking from a place at a uniform speed of 2 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
A) 4.7 kmph
B) 2.6 kmph
C) 4 kmph
D) 7 kmph
E) 5.3 kmph
A) 4.7 kmph
B) 2.6 kmph
C) 4 kmph
D) 7 kmph
E) 5.3 kmph
24 Aug 2013, 23:53
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rrsnathan
Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 2 + 5/9
= 2.55
Answer B
taransambi
GMAT 2: 680 Q45 V38
Posts: 13
09 Sep 2013, 22:14
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A start walking from a place at a uniform speed of 2 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
A) 4.7 kmph
B) 2.6 kmph
C) 4 kmph
D) 7 kmph
E) 5.3 kmph
In half an hour, A will travel 1 km. B catches A in 1 hour 48 minutes, which means A traveled for another 1 hr 48 min in addition to 30 min that he had traveled before B started his journey. So, A travels for a total of 2 hours 18 min.
For A: 1km (30 min) + 2km (1hour) + {(4/5)*2}km in 48 min (48 min are 4/5th of an hour) = 1+2+(8/5) = 23/5 km
B travels for 1 hr 48 min. And he covers 23/5 km in that time. You have the time and the distance. Let's use Rxt=D formula for a quick calculation. 1 hr 48 min can be written as 1 4/5 hours or 9/5. So B's Rate = (23/5)/(9/5) = 23/5 = 2. something. Only option B has a 2. something. So B is the correct answer.
This can be done fairly quickly of course, but had to be a long post to explain properly.
Another Method: Quick guessing - A travels for roughly 2 hours at a rate of 2 km per hour for a total of 4 km. B covers 4 km in roughly 2 hours, so his rate has to be close to 2 kmh. None of the answers except B are close to 2. If some were, we could have looked a little deeper to see that A traveled for slightly more than 2 hours, therefore slightly more than 4km. B traveled a little less than 2 hours. So the ratio will be slightly more than 2. Hence B.
A) 4.7 kmph
B) 2.6 kmph
C) 4 kmph
D) 7 kmph
E) 5.3 kmph
In half an hour, A will travel 1 km. B catches A in 1 hour 48 minutes, which means A traveled for another 1 hr 48 min in addition to 30 min that he had traveled before B started his journey. So, A travels for a total of 2 hours 18 min.
For A: 1km (30 min) + 2km (1hour) + {(4/5)*2}km in 48 min (48 min are 4/5th of an hour) = 1+2+(8/5) = 23/5 km
B travels for 1 hr 48 min. And he covers 23/5 km in that time. You have the time and the distance. Let's use Rxt=D formula for a quick calculation. 1 hr 48 min can be written as 1 4/5 hours or 9/5. So B's Rate = (23/5)/(9/5) = 23/5 = 2. something. Only option B has a 2. something. So B is the correct answer.
This can be done fairly quickly of course, but had to be a long post to explain properly.
Another Method: Quick guessing - A travels for roughly 2 hours at a rate of 2 km per hour for a total of 4 km. B covers 4 km in roughly 2 hours, so his rate has to be close to 2 kmh. None of the answers except B are close to 2. If some were, we could have looked a little deeper to see that A traveled for slightly more than 2 hours, therefore slightly more than 4km. B traveled a little less than 2 hours. So the ratio will be slightly more than 2. Hence B.
