James is painting a wooden slat fence he had installed around his backyard. The fence has a total of 180 wooden slats. Suppose James is able to paint 2 slats every 5 minutes. His friend Gabe offers to help him. Together, they finish painting the fence in 3 hours 20 minutes.At what rate did Gabe paint the fence?

Question

cristalvargas1718 cristalvargas1718

14-03-2020
Mathematics

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James is painting a wooden slat fence he had installed around his backyard. The fence has a total of 180 wooden slats. Suppose James is able to paint 2 slats every 5 minutes. His friend Gabe offers to help him. Together, they finish painting the fence in 3 hours 20 minutes.At what rate did Gabe paint the fence?

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walber000 walber000 · Answer 1 · 2020-03-17T02:44:06+01:00

Answer:

1 slat every 2 minutes.

Step-by-step explanation:

James is able to paint 2 slats every 5 minutes.

James and Gabe together are able to paint the whole fence (180 slats) in 3 hours and 20 minutes (200 minutes)

The rate of 180 slats in 200 minutes is equal to 18 slats in 20 minutes, and is equal to 9 slats in 10 minutes.

The rate of James is 2 slats in 5 minutes, which is equal to 4 slats in 10 minutes.

Subtracting the rate of James and Gabe together (9 slats in 10 minutes) by the rate of James alone (4 slats in 10 minutes), we have the rate of Gabe, which is 5 slats in 10 minutes, or 1 slat in 2 minutes.