SOLUTION: a boy went out into the barangay on his bike at 5 kph. He rested for 2 hours and returned home at the rate of 3 kph. if he was gone for 6 hours how far did he go?

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Question 889930: a boy went out into the barangay on his bike at 5 kph. He rested for 2 hours and returned home at the rate of 3 kph. if he was gone for 6 hours how far did he go?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The time actually spent biking was:
+6+-+2+=+4+
Let +d+ = his one-way distance
Let +t+ = time in hrs spent biking at +5+ km/hr
+4+-+t+ = time in hrs spent biking at +3+ km/hr
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given:
(1) +d+=+5t+
(2) +d+=+3%2A%28+4+-+t+%29+
--------------------
By substitution:
(2) +5t+=+3%2A%28+4+-+t+%29+
(2) +5t+=+12+-+3t+
(2) +8t+=+12+
(2) +t+=+3%2F2+
------------------
(1) +d+=+5t+
(1) +d+=+5%2A%283%2F2%29+
(1) +d+=+15%2F2+
The total distance was:
+15%2F2+%2B+15%2F2+=+15+
The boy went 15 km
---------------------
check:
(2) +d+=+3%2A%28+4+-+t+%29+
(2) +15%2F2+=+3%2A%28+4+-+3%2F2+%29+
(2) +15%2F2+=+3%2A%285%2F2%29+
(2) +15%2F2+=+15%2F2+
OK