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Ilia_Sergeevich [38]
3 years ago
14

Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if

Jane can eat a pizza 5 seconds faster than Dien?
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

Answer:

  • Dien - 15 seconds, Jane - 10 seconds

Step-by-step explanation:

<u>Together:</u>

  • 2/3 of pizza ⇒ 4 seconds
  • Full pizza ⇒ 4 ÷ 2/3 = 6 seconds

Dien needs  x seconds to eat pizza

Jane needs  x - 5 seconds to eat pizza

<u><em>In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza</em></u>

  • 1/x + 1/(x - 5) = 1/6
  • x(x - 5) = 6(x + x - 5)
  • x² - 5x - 12x + 30 = 0
  • x² - 17x + 30 = 0
  • (x - 15)(x - 2) = 0
  • x = 15 (x = 2 is discounted as not realistic)

Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds

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