taransambi wrote:
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.
B's rate would be 23/9 not 23/5.
Your explanation is simple and neat. +1