Matt, Phoebe, Geo, and Ruby form a straight line. Geo is exactly in the middle of Matt and Phoebe. On the other hand, Ruby is between Matt and Phoebe. The ratio of the distance of Matt and Ruby to the distance of Ruby and Phoebe is 13 : 5 . If Matt is 36 ft away from Geo, how far is Ruby from Matt and from Phoebe, respectively?
Answer:
Ruby is 20 ft away from Phoebe. On the other hand, Ruby is 52 ft away from Matt.
Step-by-step explanation:
Step 1: Write the given:
- Geo is exactly in the middle of Matt and Phoebe.
- Matt is 36 ft away from Geo.
- Ruby is also in the middle of Matt and Phoebe however the ratio of the distance of Matt and Ruby to Ruby and Phoebe is 13:5.
Step 2: Determine the distance between Matt and Phoebe
- Since the distance between Matt and Geo is 36 ft, then the distance from Geo and Phoebe is also 36 ft.
- Then the distance between Matt and Phoebe is twice that of the distance between Matt and Geo, which is 72 ft.
Step 3: Determine the distance of Ruby from Matt and Phoebe.
- Since the ratio of distance of Matt and Ruby to Ruby and Phoebe is 13:5, divide the 72 ft to 18 parts (13+5).
- 72 ft divided to 18 parts is 4 ft.
- 13 parts multiplied to 4 ft is 52 ft
- 5 parts multiplied to 4 ft is 20 ft
- Ruby is closer to Phoebe than Matt
- Ruby is 20 ft from Phoebe and 52 ft from Matt.
Therefore, Ruby is 20 ft from Phoebe and 52 ft from Matt.
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