Barcallica Posted June 7, 2012 Report Share Posted June 7, 2012 A truck travels from A to B. Going uphill, it goes at 56 mph. Going downhill, it goes at 72 mph. On level ground, it goes at 63 mph. If it takes 4 hours to travel from A to B, and 5 hours to come back, what is the distance between A and B? Quote Link to comment Share on other sites More sharing options...
0 kevink2 Posted June 7, 2012 Report Share Posted June 7, 2012 (edited) 283.5Mi 252 miles of it is downhill from A to B and 31.5 miles are flat. It takes 1/2 hour to go the flat part (31.5 mi/63mi/hour) For the downhill portion , it takes 3.5 hours (252/72) Going back (uphill) it takes 4.5 hours (252/56) Edited June 7, 2012 by kevink2 Quote Link to comment Share on other sites More sharing options...
0 Potok Posted June 7, 2012 Report Share Posted June 7, 2012 (edited) Same answer here, is ofc correct. 72*t = 56 * (t+1) .. t=3,5h, the time it takes to drive downhill from A to B, rest is just filling the gaps Edited June 7, 2012 by Potok Quote Link to comment Share on other sites More sharing options...
0 Barcallica Posted June 7, 2012 Author Report Share Posted June 7, 2012 283.5Mi 252 miles of it is downhill from A to B and 31.5 miles are flat. It takes 1/2 hour to go the flat part (31.5 mi/63mi/hour) For the downhill portion , it takes 3.5 hours (252/72) Going back (uphill) it takes 4.5 hours (252/56) Same answer here, is ofc correct. 72*t = 56 * (t+1) .. t=3,5h, the time it takes to drive downhill from A to B, rest is just filling the gaps turned out to be so easy I guess. well done Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted June 7, 2012 Report Share Posted June 7, 2012 (edited) Interesting! I got the same answer..., 0 miles flat 15.75 miles downhill (from A toward B) 267.75 miles uphill (from A toward B) Edited June 7, 2012 by CaptainEd Quote Link to comment Share on other sites More sharing options...
0 Potok Posted June 7, 2012 Report Share Posted June 7, 2012 So in your solution A is lower (compared to sea level) than B and you travel from A to B mostly uphill ? But the path from A to B is (timewise) shorter than from B to A. Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted June 7, 2012 Report Share Posted June 7, 2012 Suppose D is the distance traveled downhill from A to B, L is the distance traveled on level ground from A to B, and U is the distance traveled uphill from A to B. Then the total time to travel from A to B is (D/72)+(L/63)+(U/56)=4. We can multiply through by 504 to get 7D+8L+9U=2016 (call this equation X). On the way back from B to A, D and U switch roles, with D being uphill and U being downhill. So, for the return trip, we get (D/56)+(L/63)+(u/72)=5. Multiply both sides by 504 to get 9D+8L+7U=2520. Adding this to equation X gives 16D+16L+16U=4536. Simplify this to D+L+U=283.5. Since D+U+L is the distance from A to B, we have determined that distance to be 283.5 without specifying what D, L, and U are. Note that this problem only has a unique solution for some sets of speeds. {D=72,L=63,U=56} happens to be one such set. 1 Quote Link to comment Share on other sites More sharing options...
0 CaptainEd Posted June 7, 2012 Report Share Posted June 7, 2012 So in your solution A is lower (compared to sea level) than B and you travel from A to B mostly uphill ? But the path from A to B is (timewise) shorter than from B to A. Oops, you're right, I got it backward. Quote Link to comment Share on other sites More sharing options...
0 ujjagrawal Posted June 8, 2012 Report Share Posted June 8, 2012 Here is one way to solve this... Quote Link to comment Share on other sites More sharing options...
0 ujjagrawal Posted June 8, 2012 Report Share Posted June 8, 2012 x/63 + y/72= 4 x/63 + y/56= 5 x = 31.5 Mi ; net ground level distance. y = 252 Mi ; net inclined distance Total x + y = 283.5 Mi. Quote Link to comment Share on other sites More sharing options...
0 bhramarraj Posted June 8, 2012 Report Share Posted June 8, 2012 Suppose D is the distance traveled downhill from A to B, L is the distance traveled on level ground from A to B, and U is the distance traveled uphill from A to B. Then the total time to travel from A to B is (D/72)+(L/63)+(U/56)=4. We can multiply through by 504 to get 7D+8L+9U=2016 (call this equation X). On the way back from B to A, D and U switch roles, with D being uphill and U being downhill. So, for the return trip, we get (D/56)+(L/63)+(u/72)=5. Multiply both sides by 504 to get 9D+8L+7U=2520. Adding this to equation X gives 16D+16L+16U=4536. Simplify this to D+L+U=283.5. Since D+U+L is the distance from A to B, we have determined that distance to be 283.5 without specifying what D, L, and U are. Note that this problem only has a unique solution for some sets of speeds. {D=72,L=63,U=56} happens to be one such set. Suppose D is the distance traveled downhill from A to B, L is the distance traveled on level ground from A to B, and U is the distance traveled uphill from A to B. Then the total time to travel from A to B is (D/72)+(L/63)+(U/56)=4. We can multiply through by 504 to get 7D+8L+9U=2016 (call this equation X). On the way back from B to A, D and U switch roles, with D being uphill and U being downhill. So, for the return trip, we get (D/56)+(L/63)+(u/72)=5. Multiply both sides by 504 to get 9D+8L+7U=2520. Adding this to equation X gives 16D+16L+16U=4536. Simplify this to D+L+U=283.5. Since D+U+L is the distance from A to B, we have determined that distance to be 283.5 without specifying what D, L, and U are. Note that this problem only has a unique solution for some sets of speeds. {D=72,L=63,U=56} happens to be one such set. Well said....! Another unique sets of speeds is D=56, U=42, L=48. In this case (If time of travell remains same); Two equations will be: 6D+7L+8U=6*7*8*4 8D+7L+6U=6*7*8*5 Adding both equations we get: 14(D+L+U)= 6*7*8*9 Therefore D+L+U=216 Quote Link to comment Share on other sites More sharing options...
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Barcallica
A truck travels from A to B.
Going uphill, it goes at 56 mph.
Going downhill, it goes at 72 mph.
On level ground, it goes at 63 mph.
If it takes 4 hours to travel from A to B, and 5 hours to come back,
what is the distance between A and B?
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