I set this problem up so you can almost stumble upon the solution accidentally by playing with the numbers I gave. If you see that in 1 hour's time they both cover the same amount of miles as their speed in miles per in an hour. In this case Bill traveled 3.5 miles in 1 hour and Susie 1.5 miles in 1 hour. You might have also stumbled upon the fact that this number when added equals the distance of the track which was 5 miles. This means that if they together covered a distance of 5 miles then that's when they "meet"-- so, coincidentally this is the answer for the 1st & 2nd parts of the problem. Bill goes 3.5 miles (distance) and Susie 1.5 miles (distance) when they meet each other in the 1 hour (time). Whether or not they kept going after their argument is another story.

A pure algebraic solution would use this scenario and just add the respective speeds together so 3.5x + 1.5x = 5 , where x is the speed in miles/hour and 5 is the distance in miles. You can do this when you realize that if something is moving towards you at a given speed say 30 miles and your moving 60 miles/hour its as though you're moving towards an object standing still at 90 miles/hour. In other words, you can figure the time you cover a respective distance in relation to another person moving towards you just by adding the 2 speeds and figuring out the time it would take you to cover that distance with that new "added up" speed. So, 5x = 5 which means x = 1 hour*. Substituting back in the problem 3.5(1) + 1.5(1) = 5 =.... 5 = 5, which is correct. So, Bill went 3.5 miles and Susie 1.5 miles when they met in 1 hours time.

*When you divide miles by miles/hour the miles cancel and your left with the hours.....

## Saturday, March 8, 2008

### Time and Distance Problem 1 Solution

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