Guest Posted February 20, 2008 Report Share Posted February 20, 2008 A car travels downhill at 72 km per hr, on the level at 63 km per hr, and uphill at 56 km per hr. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What is the distance between the two towns. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 20, 2008 Report Share Posted February 20, 2008 273 km Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 20, 2008 Report Share Posted February 20, 2008 (edited) 273km Solution: (40minutes/60minutes) = Conversion to hours Ratio between the two speeds (uphill:downhill) = 72/56 So, 72/56x - 1x = (40/60) Or (72/56-1)x = (40/60) (40/60)/(72/56-1) = x x = 2 1/3hrs Plug and chug to verify 72km per hr for 2 1/3 hours = 168 km Remaing time of 1 2/3 hours at 63 km = 105 Reverse way: 56 km per hour for a distance of 168 km = 3hours and the other time was 1 2/3 which equals 4 hours, 40 minutes Hope my explanation is clear Edited February 20, 2008 by PolishNorbi Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted February 20, 2008 Report Share Posted February 20, 2008 A car travels downhill at 72 km per hr, on the level at 63 km per hr, and uphill at 56 km per hr. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What is the distance between the two towns. Can we assume that the road from A to B has a constant grade? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 21, 2008 Report Share Posted February 21, 2008 Can we assume that the road from A to B has a constant grade? Bonanova, I think you don't need to assume that A to B have constant grade, but you do need to assume (or maybe its given) that he drives at constant speed of 72kmph downhill, regardless of the gradient and 56kmph uphill regardless of the gradient . Let's say that there is x km of downhill, y km of level and z km of uphill from A to B and that the car accelerates infinitely between such changes of gradient and that he drives at constant speed of 72kmph downhill, regardless of the gradient and 56kmph uphill regardless of the gradient . To find: x+y+z = d Going from A to B: --- (i) x/72+y/63+z/56 = 4 => 7x+8y+9z = 2016 Going from B to A: --- (ii) x/56+y/63+z/72 = 4.67 => 9x+8y+7z=2352 Adding (i)+(ii) 16(x+y+z) = 4368 Therefor, d = 273 km Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 21, 2008 Report Share Posted February 21, 2008 Can we assume that the road from A to B has a constant grade? You may assume that the car travels at constant speed during the three events. That is, at constant speed of 72 km per hr on the downhill, at 63 km per hr on the level, and at 56 km per hr on the uphill. Quote Link to comment Share on other sites More sharing options...
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A car travels downhill at 72 km per hr, on the level at 63 km per hr, and uphill at 56 km per hr. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What is the distance between the two towns.
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