Question 1194493: Please help me solve this :
Gordon rode his bike at 15 mph to get his car. He then drove back at 45
mph. If the entire trip took him 8 hours, how far away was his car?
Please Include Represent, Relate, Equate, Solve and Prove. Thank you very much!
Found 4 solutions by Theo, Alan3354, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! r = rate
t = time
d = distance
formula is r * t = d
the total time going and coming back is 8 hours.
for gordon going, the formula becomes 15 * t = d
for gordon coming back, the formula becomes 45 * (8 - t) = d
since they both = d, then 15 * t = 45 * (8 - t)
simplify to get:
15 * t = 360 - 45 * t
add 45 * t to both sides of the equation to get:
60 * t = 360
solve for t to get:
t = 6
the original formulas become:
15 * 6 = d which becomes 90 = d
45 * (8 - 6) = d which becomes 45 * 2 = d which becomes 90 = d
his car is 90 miles away.
that's your answer.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Gordon rode his bike at 15 mph to get his car. He then drove back at 45
mph. If the entire trip took him 8 hours, how far away was his car?
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Average speed of a round trip is
2*v1*v2/(v1+v2) = 2*15*45/60 = 22.5 mi/hr
RT distance = 22.5*8 = 180 miles
Distance = 90 miles
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The formula for avg speed of a round trip is similar to parallel resistors, parallel flow, parallel work, etc.
Only the factor of 2 is different.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The ratio of speeds is 15:45 = 1:3, and the distances are the same, so the ratio of times spent at the two speeds is 3:1.
3x = hours spent riding
x = hours spent driving
3x+x=8
4x=8
x=2
hours spent riding at 15mph = 3x = 6
hours spent driving at 45mph = x = 2
distance riding (rate times time): 6(15) = 90
distance driving: 2(45) = 90
ANSWER: 90 miles
Answer by josgarithmetic(39617)  (Show Source):
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