Question
During a bike challenge, riders have to collect various colored ribbons. Each 1/2 mile they collect a red ribbon, each 1/8 mile they collect a green ribbon, and each 1/4 mile they collect a blue ribbon. Which colors of ribbons will be collected at the 3/4 mile marker?
Answer:
A green and a blue ribbon will be collected at the \(\frac{3}{4}\) mile marker.
Step-by-step explanation:
Topic: Factors and Multiples
To solve this, we'll write out the first few multiples of the distances where the collection of ribbons occurs:
Given that each \(\frac{1}{2}\) mile they collect a red ribbon; The multiples for the Red Ribbon are as follows (by adding \(\frac{1}{2}\) at each progression):
Red: \(\frac{1}{2} -> {1}{} -> \frac{3}{2} -> {2}{} -> \frac{5}{2}\)
Given that each \(\frac{1}{8}\) mile they collect a green ribbon; The multiples for the Green Ribbon are as follows (by adding \(\frac{1}{8}\) at each progression):
Green: \(\frac{1}{8} -> \frac{1}{4} -> \frac{3}{8} -> \frac{1}{2} -> \frac{5}{8} -> \frac{3}{4} -> \frac{7}{8} -> {1}\)
Given that each \(\frac{1}{4}\) mile they collect a blue ribbon; The multiples for the Blue Ribbon are as follows (by adding \(\frac{1}{4}\) at each progression):
Blue: \(\frac{1}{4} -> \frac{1}{2} -> \frac{3}{4} -> {1}\)
Since , \(\frac{3}{4}\) is a multiple of both \(\frac{1}{8} and \frac{1}{4}\) , then a green and a blue ribbon will be collected at the \(\frac{3}{4}\) mile marker.
