SOLUTION: A cyclist rides 600 meters up a hill and 400 meters down the other side. his speed is twice as fast downhill as uphill and the whhole journey takes 4 minutes. how long does it take

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Question 573698: A cyclist rides 600 meters up a hill and 400 meters down the other side. his speed is twice as fast downhill as uphill and the whhole journey takes 4 minutes. how long does it take him to reach the summit?
My working out
Distance over time= speed so the total journey is 1000 meters and the total time is 4 minutes(240 seconds)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed going uphill ( m/min )
+2s+= his speed going downhill ( m/min )
Let +t+ = His time going up hill ( min )
+4+-+t+ = his time going downhill ( min )
--------------------------------
uphill:
(1) +600+=+s%2At+
downhill:
(2) +400+=+2s%2A%28+4+-+t+%29+
-------------------
(1) +s+=+600%2Ft+
Substitute (1) into (2)
(2) +400+=+2%2A%28+600%2Ft+%29%2A%284+-+t+%29+
(2) +400+=+%28+8+-+2t+%29%2A%28600%2Ft%29+
(2) +400+=+4800%2Ft+-+1200+
(2) +400t+=+4800+-+1200t+
(2) +1600t+=+4800+
(2) +t+=+3+
It takes him 3 minutes to reach the summit
check:
(1) +s+=+600%2Ft+
(1) +s+=+600%2F3+
(1) +s+=+200+
and
(2) +400+=+2s%2A%28+4+-+t+%29+
(2) +400+=+2%2A200%2A%28+4+-+3+%29+
(2) +400+=+400+
OK