SOLUTION: Word Problem: Two cyclists, 50 miles aprt, are racing towards each other from opposite directions at constant speeds of 18mph and 22mph. A fly buzzes back and forth between the

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Word Problem: Two cyclists, 50 miles aprt, are racing towards each other from opposite directions at constant speeds of 18mph and 22mph. A fly buzzes back and forth between the      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 566594: Word Problem:
Two cyclists, 50 miles aprt, are racing towards each other from opposite directions at constant speeds of 18mph and 22mph. A fly buzzes back and forth between the noses of the cyclists at 100mph until it is smashed when the cyclists collide. How far did the fly travel before it died?
* i dont know how to slove this problem. I know how to solve it if they collide in the middle, but in this case, they dont. Can you please help? Thank you.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The most difficult part of this problem involves not getting too twisted around trying to figure out how far the fly is traveling back and forth between the two riders as they close in on each other.
.
The thing to do is to realize that the closing speed of the two riders is the sum of their individual speeds. One rider is going 18 mph and the other is going 22 mph. That means that they are closing at a rate of 18 + 22 = 40 mph. At that combined rate they will need 1.25 hours to cover the 50 miles between them when they started out. (This comes from dividing the combined rate of 40 mph into the distance of 50 miles.) If this isn't clear, you can multiply the 18 mph of one rider times the 1.25 hours to get that the distance he travels is 22.5 miles. Then you can multiply the 22 mph of the other rider times 1.25 hours to get his distance traveled as 27.5 miles. Adding the two distances of 22.5 and 27.5 you find that the total is the 50 miles originally between the riders. This confirms that it takes the two riders 1.25 hours to collide.
.
For the total time of 1.25 hours the fly is airborne and is zipping along at a steady rate of 100 mph. (You don't need to consider in what direction the fly is traveling at any given time. You just need to realize that it is flying at 100 mph for 1.25 hours.) To get the total distance that the fly travels, just multiply its rate (100 mph) times the time it flies (1.25 hours) and you get the answer of 125 miles.
.
Hope this analysis helps you to understand the problem and how to solve it.