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 July 9th, 2018, 03:09 AM #1 Senior Member   Joined: Aug 2014 From: India Posts: 470 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
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Quote:
 Originally Posted by Ganesh Ujwal 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?
Can the car meet any bike that has completed its journey before the car starts its journey?

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: 20,978 Thanks: 2229 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
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Quote:
 Originally Posted by skipjack 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, 10:02 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 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
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Quote:
 Originally Posted by Ganesh Ujwal 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?

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
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Quote:
 Originally Posted by Denis A bike starts from Delhi going to Agra every 45 minutes, the first one starting at 8:30am, the last one at 5:30pm.
8:30,9:15,10:00,10:45,11:30,12:15,1:00,1:45,2:30,3 :15,4:00,4:45,5:30 = 13 bikes

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: 14,597 Thanks: 1038 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
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Quote:
 Originally Posted by Denis (1730 - 830)/75 + 1 = 900/75 + 1 = 12 + 1 = 13
Why did you wrote 75?

 July 10th, 2018, 05:00 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 75 represents 75% of 60 minutes: .75*60 = 45 minutes Thanks from Ganesh Ujwal

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