SOLUTION: Three friends Smith, Jack and Pamila are walking at the speed of 3, 4, 5 km/h respectively. They start from same place at 1pm, 2pm and 3pm respectively. When Jack reaches Smith, he

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Question 951797: Three friends Smith, Jack and Pamila are walking at the speed of 3, 4, 5 km/h respectively. They start from same place at 1pm, 2pm and 3pm respectively. When Jack reaches Smith, he sends him back with a message for Pamila. At what time will Pramila get the message.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
From 1 PM to 2 PM is 1 hr
Smith travels:
+d%5B1%5D+=+3%2A1+
+d%5B1%5D+=+3+ km
----------------
I start a stopwatch when Jack leaves,
and stop it when Jack catches Smith,
Let +d%5B2%5D+ = distance Jack travels
until Jack catches Smith
Let +t%5B2%5D+ = time in hrs for
Jack to catch Smith
----------------------------
Smith's equation:
(1) +d%5B2%5D+-+3+=+3t%5B2%5D+
Jack's equation:
(2) +d%5B2%5D+=+4t%5B2%5D+
---------------------
Substitute (2) into (1)
(1) +4t%5B2%5D+-+3+=+3t%5B2%5D+
(1) +t%5B2%5D+=+3+ hrs
and
(2) +d%5B2%5D+=+4t%5B2%5D+
(2) +d%5B2%5D+=+4%2A3+
(2) +d%5B2%5D+=+12+ km
---------------------
+1+%2B+3+=+4+ hrs have passed
since 1 PM
That means Pamela left 1 hr ago
at 3 PM
In +1+ hr, she travels:
+d%5B3%5D+=+5%2A1+
+d%5B3%5D+=+5+ km
------------------
That means she is +12+-+5+=+7+ km
behind Smith when Smith turns around
+d%5B4%5D+ = distance Smith travels until they meet
+t%5B4%5D+ = time in hrs until they meet
----------------------------------
Smith's equation:
(1) +d%5B4%5D+=+3t%5B4%5D+
Pamela's equation:
(2) +7+-+d%5B4%5D+=+5t%5B4%5D+
----------------------
Substitute (1) into (2)
(2) +7+-+3t%5B4%5D+=+5t%5B4%5D+
(2) +8t%5B4%5D+=+7+
(2) +t%5B4%5D+=+7%2F8+
------------------------
Add the +4+ hrs since Smith left
to +7%2F8+ hrs until they meet
+%287%2F8%29%2A60+=+52.5+
1 PM + 4 hrs 52.5 min =
52 min 30 sec after 5 PM is the time
when Pamela gets the message
------------------
Hope I got it!




Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Three friends Smith, Jack and Pamila are walking at the speed of 3, 4, 5 km/h respectively. They start from same place at 1pm, 2pm and 3pm respectively. When Jack reaches Smith, he sends him back with a message for Pamila. At what time will Pramila get the message.
Time Pamila got message: highlight_green%285%3A15%29 PM       

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