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| Time And Distance Problem (II) (Posted on 2006-12-29) |
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P and Q are two stations 34 kilometres apart. Rick starts from P precisely at 12 noon and walks toward Q at the constant rate of 4 kilometres per hour. After journeying on for 3/2 hours he takes a rest for another 3/2 hours and then resumes his journey at the constant rate of 5 kilometres per hour.
Saul leaves Q exactly 2 hours after Rick leaves P and travels at a constant rate of 5 kilometres per hour for 2 hours. He (Saul) then takes rest for one hour before resuming his journey (towards P) at the constant rate of 4 kilometres per hour.
When and where will Rick and Saul meet? What was the distance between them at 3:00 PM? Determine when Rick and Saul were 8 kilometres apart for the first time.
Note: Rick and Saul keep on walking after they meet until they reach their respective destinations.
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Submitted by K Sengupta
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Rating: 3.5000 (2 votes)
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Solution:
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(i) Rick and Saul will meet (20 + 4/9) kilometres from station P at 53 minutes 20 seconds past 5 PM
(ii) At 3:00 PM, the distance between them was 23 kilometres.
(iii) At precisely 5:00 PM, the Rick and Saul were 8 Kilometres apart for the first time.
EXPLANATION:
The following tables display the respective movements of Rick and Saul upto 5:00 PM.
RICK
Time ................. Distance from P
12:00 Noon ......... 0 kilometres
1:30 PM............... 6 kilometres
3:00 PM .............. 6 kilometres
4:00 PM............... 11 kilometres
5:00 PM............... 16 kilometres
SAUL
Time................ Distance from Q
2:00 PM ............ 0 kilometres
3:00 PM............. 5 kilometres
4:00 PM............. 10 kilometres
5:00 PM............. 10 kilometres
From the above tables, we observe that the distance between Rick and Saul at 3:00 PM was (34 -6 - 5) = 23 kilometres.
Also, from the said tables, we observe that at 5:00 PM; Rick and Saul together covered (10 + 16) = 26 kilometres and so, they were precisely (34- 26) = 8 kilometres apart for the first time.
If they keep on walking, at precisely 6:00 PM Rick and Saul will together cover (21 + 14) = 35 kilometres. In other words they will have reached their respective destinations before 6:00 PM.
Consequently, they will together cover a total distance of 34 kilometres precisely (34-26)/(5+4) = 8/9 hours = 53 minutes 20 seconds past 5:00 PM.
Now, after 5:00 PM, Rick will cover an additional (8/9)*5 = (4+4/9) kilometres before he meets up with Saul.
Hence, Rick and Saul will meet for the first time at 53 minutes 20 seconds past 5:00 PM , precisely (20+ 4/9) kilometres from P.
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