Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding. a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.

b. What are the speeds of the two cyclists?

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  a) r + (r+3) = 68/4 . . . . equation to answer the question

  b) r = 7, r+3 = 10 . . . miles per hour

Step-by-step explanation:

a. The combined speed of the two cyclists is found from the time it takes for them to close the distance between them. The faster cyclist is traveling at (r+3) miles per hour.

  speed = distance/time

  r + (r+3) = 68/4 . . . . an equation to answer the problem

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b. Solving the above equation helps us answer the question

  2r +3 = 17 . . . simplify

  2r = 14 . . . . . subtract 3

  r = 7 . . . . . . divide by 2

  r+3 = 10

The speeds of the two cyclists are 7 miles per hour and 10 miles per hour.