studiot Posted October 5, 2014 Share Posted October 5, 2014 Some may have seen this before, but I thought it was a good one. Person A left Town X at 10:18 am. He walked at a constant speed and arrived at town Z at 1:30 pm. On the same day, Person B left town Z at 9 am. Person B walked the same route in the opposite direction at a constant speed. Person B arrived at town X at 11:40 am. The road crosses a wide river. By coincidence, both arrived at the bridge on opposite sides of the river at the same instant. Person A left the bridge 1 minute later than Person B. At what time did they arrive at the bridge? Link to comment Share on other sites More sharing options...
imatfaal Posted October 6, 2014 Share Posted October 6, 2014 does this look right? I make it 11:00 slight typo on second last eq Link to comment Share on other sites More sharing options...
studiot Posted October 6, 2014 Author Share Posted October 6, 2014 imatfaal does this look right? Well your answer is correct, I didn't wade through your maths yet. Well done. Link to comment Share on other sites More sharing options...
MonDie Posted October 6, 2014 Share Posted October 6, 2014 (edited) speeds = 0.83333:1 1 minute = 1 - 0.83333 = .16666 bridge trip A = 6 minutes bridge trip B = 5 minutes relative bridge distance = bridge time B / entire time B = 5/160 = 1/32 X/Z = distance from x/z to bridge x+z+0.03125 = 1 1-x = z+0.03125 -x = z−0.96875 x = -z + 0.96875 In B-relative time, A began 78/160 after B. z/1 = time for B to reach x/.83333 = time for A to reach z - 78/160 = x/.83333 x = (z-.4875)*.83333 I need the intersection of these two lines, but my calculator won't find it for me. I'll see whether I can do it with wxMaxima. The value of z at the intersection multiplied by 160 should give the amount of minutes it took B to reach the bridge. My calculator won't finish it, and wxMaxima can only plot 1 line at a time. Edited October 6, 2014 by MonDie Link to comment Share on other sites More sharing options...
studiot Posted October 6, 2014 Author Share Posted October 6, 2014 Interesting iterative approach, Mondie. Looks promising. Link to comment Share on other sites More sharing options...
MonDie Posted October 6, 2014 Share Posted October 6, 2014 (edited) Your thoughtfulness is noted. I think "Solve" is the wxMaxima tool I wanted. (10999987÷14666640)×160 = 120 = 2 hours B (and A) reached the bridge at 11:00. Before looking at imatfaal's post, I acidentally put 10:20 as if there were 100 minutes in an hour!! Edited October 6, 2014 by MonDie Link to comment Share on other sites More sharing options...
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