July 9th, 2018, 03:09 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  How to solve this puzzling type time and distance model problem?
A bike starts from Delhi every 45 minutes, the first one starting at 8:30 am, and the last one starting at 5:30pm. A car starts from Agra every 60 minutes, the first one starting at 10am and the last at 4 pm. A bike takes 5 hours and a car takes 4 hours to cover the distance. How many bikes would a car that starts at 2 pm meet in the way? Solution: I can tell that from 8:30 am to 5:30pm, 12+1= 13 bikes left for destination. after this How to proceed from cars side? 
July 9th, 2018, 03:30 AM  #2  
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  Quote:
Can the car meet any bike that does not start its journey until after the car has finished its journey? So what next?  
July 9th, 2018, 08:05 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1752 
As 9 hours / 45 minutes = 12, there are 12 bikes that leave Delhi after 9 am (so that they arrive in Agra after 2 pm) and before 6 pm.

July 9th, 2018, 08:09 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  
July 9th, 2018, 10:02 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,542 Thanks: 1752 
You didn't ask about cars (plural). You asked how many bikes would be met by a particular car that sets out at 2 pm, and then asked how to proceed from cars side (which isn't a question that asks explicitly about a number of cars). If you want to find out how many cars would be met by a particular bike, you didn't make that clear, but that would be tackled by the method I posted for the "how many bikes" question. 
July 9th, 2018, 01:27 PM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,133 Thanks: 914  Quote:
A bike starts from Delhi going to Agra every 45 minutes, the first one starting at 8:30am, the last one at 5:30pm. A car starts from Agra going to Delhi at 2:00pm. A bike takes 5 hours and a car takes 4 hours to cover the distance. How many bikes will the car meet on the way?  
July 9th, 2018, 08:03 PM  #7  
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  Quote:
I got total 13 bikes. Is there any formula to avoid this counting each time intervals?  
July 10th, 2018, 04:27 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,133 Thanks: 914 
Use 24hour clock; like, 3 pm = 15 Then 5:30 pm = 17:30 (1730  830)/75 + 1 = 900/75 + 1 = 12 + 1 = 13 If you can't follow that, stay out of the clock business 
July 10th, 2018, 04:40 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  
July 10th, 2018, 05:00 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,133 Thanks: 914 
75 represents 75% of 60 minutes: .75*60 = 45 minutes


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distance, model, problem, puzzling, solve, time, type 
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