July 9th, 2018, 04:09 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 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, 04:30 AM  #2  
Senior Member Joined: May 2016 From: USA Posts: 1,186 Thanks: 489  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, 09:05 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
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, 09:09 AM  #4 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
July 9th, 2018, 11:02 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,865 Thanks: 1833 
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, 02:27 PM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,451 Thanks: 947  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, 09:03 PM  #7  
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Quote:
I got total 13 bikes. Is there any formula to avoid this counting each time intervals?  
July 10th, 2018, 05:27 AM  #8 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,451 Thanks: 947 
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, 05:40 AM  #9 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  
July 10th, 2018, 06:00 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,451 Thanks: 947 
75 represents 75% of 60 minutes: .75*60 = 45 minutes


Tags 
distance, model, problem, puzzling, solve, time, type 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to solve this "time and distance" concept problem?  Ganesh Ujwal  Elementary Math  2  April 27th, 2018 11:54 AM 
Time rate distance world problem  Nrb  Algebra  6  September 9th, 2013 03:18 AM 
Distance, rate, time problem  jc90usa  Algebra  15  January 13th, 2013 11:07 AM 
Distance, speed and time problem  thinkfast  Algebra  2  January 21st, 2012 02:19 AM 
Word Problem: Find distance as a function of time.  Chaim  Calculus  1  October 27th, 2011 10:50 PM 