Question

Peter estimates that it takes him 1/4 hours to prepare dough, 1/10 hours to grate cheese, 1/3 of an hour to prepare toppings, and 2/5 an hour to bake the pizza.

What fraction of time did it take peter in total to prepare the pizza?

What was the actual time it took in minutes and hours?

Answer 1

13/12 hours

1 hour 5 minutes

Explanation:

Given timings:

• 1/4 hours to prepare dough.
• 1/10 hours to grate cheese.
• 1/3 of an hour to prepare toppings.
• 2/5 if an hour to bake the pizza.

To find the total time it took Peter to prepare the pizza, sum the fractions.

`\implies (1)/(4)+(1)/(10)+(1)/(3)+(2)/(5)`

`\implies (1 \cdot 15)/(4\cdot 15)+(1\cdot 6)/(10\cdot 6)+(1 \cdot 20)/(3\cdot 20)+(2 \cdot 12)/(5\cdot 12)`

`\implies (15)/(60)+(6)/(60)+(20)/(60)+(24)/(60)`

`\implies (15+6+20+24)/(60)`

`\implies (65)/(60)`

`\implies (13 \cdot 5)/(12 \cdot 5)`

`\implies (13)/(12)`

Therefore, it took Peter 13/12 hours to prepare the pizza.

Convert hours into minutes by multiplying the hours by 60:

`\implies (13)/(12) \cdot 60=(780)/(12)=65\; \sf minutes`

As 60 minutes = 1 hour, then:

⇒ 65 minutes = 1 hour and 5 minutes.

Therefore, the actual time it took for Peter to prepare the pizza is 1 hour and 5 minutes.

Answer 2

• 13/12 hours or 1 hour and 5 minutes

--------------------------------

Add up all fractions to get total time to prepare the pizza

• 1/4 + 1/10 + 1/3 + 2/5 = Common denominator is LCM(3,4,5,10) = 60
• 15/60 + 6/60 + 20/60 + 24/60 =
• 65/60 hours = (13/12 hours simplified fraction)
• 65 minutes =
• 1 hour and 5 minutes