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Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie?

(1) Charlie gets to the trailer in 55 minutes.

(2) Buster gets to the studio at the same time as Charlie gets to the trailer.

(1) Charlie gets to the trailer in 55 minutes. No info about Buster. Not sufficient.

(2) Buster gets to the studio at the same time as Charlie gets to the trailer. Charlie needed 20 minutes less than Buster to cover the same distance, which means that the rate of Charlie is higher than that of Buster. Since after they pass each other they need the same time to get to their respective destinations (they get at the same time to their respective destinations) then Buster had less distance to cover ahead (at lower rate) than he had already covered (which would be covered by Charlie at higher rate). Sufficient.

Can you please share your thoughts on this problem.

I have tried to visualize it this way. Say we have 100m distance between the two points. Now, See Buster has started 20 minutes before but still reaches at the same time that means his time is t + 20 if t is the time taken by charlie to reach 100 meters distance.

Now, one thing we know is that : charlie has higher speed than buster. So far so good. But how do we know what happens before they cross, at the time of crossing and after they have crossed is something I need more clarification on.

When Charlie starts Buster has already covered a distance equal to 20 times his speed in miles per hour. When charlie and Buster meet at say X point then we have D-X more than X Since if both we running at equal speed then starting 20 minutes early they would have met beyond the midpoint of the D.

Can you please share your thoughts on this problem.

I have tried to visualize it this way. Say we have 100m distance between the two points. Now, See Buster has started 20 minutes before but still reaches at the same time that means his time is t + 20 if t is the time taken by charlie to reach 100 meters distance.

Now, one thing we know is that : charlie has higher speed than buster. So far so good. But how do we know what happens before they cross, at the time of crossing and after they have crossed is something I need more clarification on.

When Charlie starts Buster has already covered a distance equal to 20 times his speed in miles per hour. When charlie and Buster meet at say X point then we have D-X more than X Since if both we running at equal speed then starting 20 minutes early they would have met beyond the midpoint of the D.

we are concerned what happens when B reaches half the distance..

B takes \(x\) min and C takes \(x-20\).... B is at half the distance at \(\frac{x}{2}\).....

so lets see where is C at this time -20 min, as he starts 20 minutes later = \(\frac{x}{2} -20\).. But when does C reach midway = at \(\frac{x-20}{2} =\frac{x}{2} - 10\) since C reaches half way ONLY at \(\frac{x}{2} -10\), he has to walk for another 10 minutes after \(\frac{x}{2}-20\) to reach mid-way.. so they meet towards the starting point of C.. suff
_________________

Thank you Chetan for your explanation. It all makes sense now. I think, logically also what bunuel said is the correct way. Suppose they were to meet at the middle point. Then in that case C would have reached the destination earlier that B. Suppose they meet at any point before the midpoint and towards B then C would have lesser distance and more rate than B, Hence C still would have reached before B. Thus, the only scenario when Both reaches at the same time is when B has already travelled considerable distance ( at least more than the half ) before C started and then C starts 20 minutes later and covers that at higher rate.

I wasn't satisfied with the explanation given here so i tried to solve it: Smart numbers worked only after doing some attempts as answer used to vary with the distance between b mph and c mph. Let me know if you think i am doing some/anything wrong...

PLEASE USE C = 19 NOT 20. as i said, the answer only made sense after a few trials...

>> !!!

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