August 29th, 2018, 12:54 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  what is the B's speed?
A and B start moving towards each other from points X and Y respectively .After they meet on the way, they take 16 seconds and 25 seconds to reach Y and X respectively. If A speed is 1.25 m/sec, what is the B's speed? I can calculate A's distance after meeting B. After that, I can't proceed. 
August 29th, 2018, 01:25 AM  #2 
Newbie Joined: Aug 2018 From: gonda Posts: 1 Thanks: 0  
August 29th, 2018, 04:19 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,882 Thanks: 1835 
I'll assume A has constant speed a m/s and B has constant speed b m/s. If A and B meet t seconds after setting out, at = 25b and 16a = bt, so 25b² = abt = 16a². As a = 1.25 is given, 25b² = 25, and so B has speed 1 m/s. 
August 29th, 2018, 04:51 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
August 29th, 2018, 05:50 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,882 Thanks: 1835 
A moves distance at m from X to where the cars meet, which is also the distance B then moves to reach X, which is 25b m. Hence at = 25b, and 16a = bt is obtained similarly.

August 29th, 2018, 05:59 AM  #6 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
August 29th, 2018, 02:04 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 19,882 Thanks: 1835 
Let M be the point where A meets B. A moves from X to M (so XM = at), then B moves from M to X (so MX = 25b). B moves from Y to M (so YM = bt), then A moves from M to Y (so MY = 16a). XM = MX implies at = 25b. YM = MY implies bt = 16a. I'm not sure how to show movement in a diagram. You could show XMY as a line, with M a bit nearer to Y than to X. 
August 29th, 2018, 07:43 PM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,479 Thanks: 950 
Practice with this one: A and B start moving towards each other from points X and Y respectively . After they meet, they take 2 hours and 18 hours to reach Y and X respectively. If A's speed is 15 m/hr, what is the B's speed? [X]A@15.............90..................>6hr.<30B@5[Y] [X]18hr.<90B@5;A@15.......30.........>2hr.[Y] 

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