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Time and DistanceA Problem..


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A and B walk around a circular track. They start at 8:00 am from the same point in opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am.(Answer- 7)
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A and B walk around a circular track. They start at 8:00 am from the same point in opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am.(Answer- 7)

 

Let's use some values to help us.

Let's say that the CIRCUMFERENCE of the track = 1 mile

 

So, if A completes 2 rounds (which is a total of 2 miles) per hour, then A is walking 2 miles per hour.

Likewise, if B completes 3 rounds (which is a total of 3 miles) per hour, then B is walking 3 miles per hour.

 

So, if A and B are walking towards each other, they are CLOSING THE GAP at a rate of 5 miles per hour (2 mph + 3 mph = 5 mph)

 

Starting at 8:00am, A and B are essentially 1 mile apart (since they are walking in different directions).

In other words, the GAP between them is 1 mile.

 

NOTE: Time = distance/rate

 

If the GAP is 1 mile, and the GAP closes at a rate of 5 miles per hour, then...

Time until A and B meet = 1/5 hours = 12 minutes

 

So, it takes 12 minutes until A and B pass each other for the first time.

This means it will take another 12 minutes until they pass each other for the second time.

And so on.

 

In other words, they pass each other every 12 minutes

 

So, how many times will they pass each other from 8am to 9:30am?

This equals 90 minutes

 

90/12 = 7.something

 

So, they will cross each other 7 times.

 

Cheers,

Brent

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