SOLUTION: At 9:00 a.m., Your friends begin hiking at 2mi/h. You begin from the same place at 9:25 a.m. You hike at 3mi/h. a. How long will you have hiked when you catch up with your frien

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: At 9:00 a.m., Your friends begin hiking at 2mi/h. You begin from the same place at 9:25 a.m. You hike at 3mi/h. a. How long will you have hiked when you catch up with your frien      Log On


   

Question 1054159: At 9:00 a.m., Your friends begin hiking at 2mi/h. You begin from the same place at 9:25 a.m. You hike at 3mi/h.
a. How long will you have hiked when you catch up with your friends?
b. At what time will you catch up with your friends?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
9:25 minus 9:00 = 25 min
25 min = ++25%2F60+ hrs
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What is your friend's head start in miles?
+d%5B1%5D+=+2%2A%2825%2F60%29+
+d%5B1%5D+=+5%2F6++ mi
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Start a stopwatch when you start hiking and
stop it when you catch up with friends
Let +t+ = time on stopwatch in hrs
Let +d+ = distance in miles you travel
until you catch up with friends
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Your equation:
(1) +d+=+3t+
Friend's equation:
(2) +d+-+5%2F6+=+2t+
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Plug (1) into (2)
(2) +3t+-+5%2F6+=+2t+
(2) +t+=+5%2F6+
and
(1) +d+=+3%2A%285%2F6%29+
(1) +d+=+5%2F2+
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(a)
You hike 2.5 mi until you catch up with friends
(b)
+5%2F6+=+50%2F60+ hrs
9:25 + 50 min = 10:15
You catch up with friends at 10:15
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check:
Your friends should cover +2.5+ mi in 25 min plus 50 min
= 75 min which is 1.25 hrs
+d+=+2%2A1.25+
+d+=+2.5+ mi
OK