Could you please help me with the following question ?
Al & Jim are travelling in opposite directions around a circular track. Al is going twice as fast as Jim. The time interval between their meetings as they pass each other is 30 sec. Al then doubles his speed and Jim reduces his speed by one-half. What will be the time interval between their meetings after they have changed their speeds ? If Al's initial speed was 60m/s what is the radius of the track ?
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Given: Al and Jim are going around a Circular track, Al's initial speed was 60m/s, implying Jim's was 30m/s.
In the original case, the time taken to pass each other is 30s. Since, Al is twice as fast, the distance covered (perimeter) is also twice as much. Hence, for Jim to cover one-thirds of the track, it takes him 30s.
This gives the perimeter of the track to be = 2700m.
Which gives the radius to be = 2700/(2*pi) = 429.718m
Now, if Al doubles his speed (120m/s) and Jim halves his speed (15m/s), we need to equate the time taken to complete their respective distances. We can see that Al is now 8 times as fast as Jim. Now, we need to find out how much time it takes Jim to cover 1/9th of the total perimeter (ie. 2700m).
Time= (2700m/9)/(15m/s) = 20s.
Hope this helped! :)