Question

If a day is 1½ hours longer than a night,what is the length of each? Assume that 1 day and 1 night together = 24 hours.

Step by step explanation.​

Answer 1

Answer:

1 day is 13 hours and 30minutes and 1 night is 10 hours and 30 minutes.

Step-by-step explanation:

Considering 1 day=12 hours and 1 night =12 hours

So, if 1 day is longer by 1 hours and 30minutes, 1 night will be short by 1 hours and 30 minutes, so it will be 1 day=13 hours and 30minutes and 1 night=10 hours and 30 minutes so it will sum up to 24 hours.

Thanks for the question! Subscribe to VIVA FFx!

Answer 2

Answer:

Required length of day is $12 \frac{3}{4} \: hours$ and length of night is $11 \frac{1}{4} \: hours$

Step-by-step explanation:

Given, 1 day and 1 night together = 24 hours.

Let length of 1 day be x hours

So, length of 1 night $= (24 - x) \: hours$

It is also given that a day is 1½ hours longer than a night

Now,

$1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} \\ = \frac{3}{2}$

So according to question,

$x - (24 - x) = \frac{3}{2} \\ 2x - 24 = \frac{3}{2}$

By cross multiplication,

$4x - 48 = 3 \\ 4x = 3 + 48 \\ 4x = 51 \\ x = \frac{51}{4} \\ x = 12 \frac{3}{4}$

So, length of day =

$12 \frac{3}{4} \: hours$

and length of the night

$= (24 - \frac{51}{4} ) \\ = \frac{24 \times 4 - 51}{4} \\ = \frac{96 - 51}{4} \\ = \frac{45}{4} \\ = 11 \frac{1}{4}$

This is a problem of equation part Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549

#SPJ2