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July 9th, 2018, 03:09 AM   #1
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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?
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July 9th, 2018, 03:30 AM   #2
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Quote:
Originally Posted by Ganesh Ujwal View Post
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?
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July 9th, 2018, 08:05 AM   #3
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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.
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July 9th, 2018, 08:09 AM   #4
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Quote:
Originally Posted by skipjack View Post
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.
I am asking about cars. Please reply about number of cars.
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July 9th, 2018, 10:02 AM   #5
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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.
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July 9th, 2018, 01:27 PM   #6
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Quote:
Originally Posted by Ganesh Ujwal View Post
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?
Your problem can be made clearer and simpler this 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?
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July 9th, 2018, 08:03 PM   #7
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Quote:
Originally Posted by Denis View Post
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?
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July 10th, 2018, 04:27 AM   #8
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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
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July 10th, 2018, 04:40 AM   #9
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Quote:
Originally Posted by Denis View Post
(1730 - 830)/75 + 1 = 900/75 + 1 = 12 + 1 = 13
Why did you wrote 75?
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July 10th, 2018, 05:00 AM   #10
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75 represents 75% of 60 minutes: .75*60 = 45 minutes
Thanks from Ganesh Ujwal
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