Question

In 10 minutes, courtney can write out four christmas cards. In the same time, Victoria can write 14 Christmas cards. If they work together, how long will it take them to write out 252 Christmas cards?

Answer 1

Courtney and Victoria can write 252 Christmas cards in 140 minutes when working together.

Step-by-step explanation:

To find out how long it will take Courtney and Victoria to write 252 Christmas cards when they work together, we need to first determine how many cards they can write in 10 minutes individually. Courtney can write 4 cards in 10 minutes, while Victoria can write 14 cards in the same time. Thus, Courtney can write 4/10 = 0.4 cards per minute, and Victoria can write 14/10 = 1.4 cards per minute. When they work together, their combined rate is 0.4 + 1.4 = 1.8 cards per minute.

To determine the total time it will take them to write 252 cards, we can divide the number of cards by their combined rate: 252 / 1.8 = 140 minutes. Therefore, it will take them 140 minutes to write out 252 Christmas cards when they work together.

Answer 2

To write 252 cards together Courtney and Victoria will take = 140 minutes or 2 hours and 20 minutes.

Step-by-step explanation:

Given:

Courtney writes 4 cards in 10 minutes

Victoria writes 14 cards in 10 minutes.

To find the time taken by them to write 252 cards working together.

Solution:

Using unitary method to determine their 1 minute work.

In 10 minutes Courtney writes = 4 cards

So,in 1 minute Courtney will write =
`(4)/(10)` cards

In 10 minutes Victoria writes = 14 cards

So,in 1 minute Victoria will write =
`(14)/(10)` cards

Now, Courtney and Victoria are working together.

So, in 1 minute, number of cards they can write together will be given as:

⇒
`(4)/(10)+(14)/(10)`

Since we have common denominators, so we can simply add the numerators.

⇒
`(18)/(10)`

Again using unitary method to determine the time taken by them working together to write 252 cards.

They can write
`(18)/(10)` cards in 1 minute.

To write 1 card they will take =
`(1)/((18)/(10))=(10)/(18)` minutes

So, for 252 cards the will take =
`(10)/(18)*252=(2520)/(18)=140` minutes

140 minutes = (60+60+20) minutes = 2 hours and 20 minutes [ As 60 minutes = 1 hour]

So, to write 252 cards together Courtney and Victoria will take = 140 minutes or 2 hours and 20 minutes.