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Bob can paint a fence in 5 hours and working with jen, the two of them can paint the same fence in 2 hours. how long would it take for jen to paint the fence alone?

Respuesta :

Bob ;

5 hours = 1 fence
1 hour = 1/5 fence

Together:
2 hours = 1 fence
1 hour = 1/2 fence

Jen:
1 hour = 1/2 - 1/5= 5/10 - 2/10 = 3/10

Find the amount of time Jen will need:
3/10 fence = 1 hour
1/10 fence = 1/3 hour
10/10 fence = 10/3 hour = 3 1/3 hours 

Answer: Jen will take 3 1/3 hours to paint the fence alone.
fichoh

Using the time and rate relation, it will take Jen alone 3.333 hours to paint the fence alone.

  • Bob's time alone = 5 hours
  • Combined time = 2 hours
  • Let Jen's time = t

Recall :

  • Rate = 1 / time

Hence,

  • Bob's rate = 1/5
  • Combined rate = 1/2
  • Jen's rate = 1/t

  • Combined rate = Jen's rate + Bob's rate
  • 1/2 = 1/5 + 1/t
  • 1/t = 1/2 - 1/5 = (5 - 2)/10 = 3/10

Therefore, Jen's time will be :

  • 1/t = 3/10
  • Solve for t
  • Cross multiply
  • 3t = 10
  • t = 10/3
  • t = 3.333 hours

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