Question

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?

Answer 1

• Dien - 15 seconds, Jane - 10 seconds

Explanation:

Together:

• 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

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

• 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