Question

if a day is 1½ hours longer than a night what is the length of each? assume that 1day at 1 night together =24

Answer 1

Answer : length of night is a hours. Length of day will be a+3/2.

a + ( a + 3/2 ) = 24
= 2a + 3/2 =24
4a = 48 - 3 =45
a = 45 / 4 = length of night

Length of day = 45/4 + 3/2 = 51/4

Answer 2

Given:

A day is 1 1/2 hour longer than the night

Day + Night = 24 hours

To Find:

The length of a day and the length of a night

Solution

Define x:

$\text{Let the length of a night be x hours long.}$

$\text{Then the day = } x + 1 \dfrac{1}{2} \text { hours}$

Find x:

Night + Day = 24 hours

$x + (x + 1\dfrac{1}{2} ) = 24$

$x + x + \dfrac{3}{2} = 24$

$2x + \dfrac{3}{2} = 24$

$2x = 24 - \dfrac{3}{2}$

$2x = \dfrac{48 - 3}{2}$

$2x = \dfrac{45}{2}$

$x = \dfrac{45}{4}$

$x = 11 \dfrac{1}{4} \text{ hours}$

Find the length of day and night:

$\text{Night } = x$

$\text{Night } = 11 \dfrac{1}{4} \text{ hours}$

$\text{Night } = 11 \text{ hours and } 15 \text{ mins}$

$\text{Day } = x + \dfrac{3}{2}$

$\text{Day } = 11\dfrac{1}{4} + \dfrac{3}{2}$

$\text{Day } = 11\dfrac{1 + 6}{4}$

$\text{Day } = 11\dfrac{7}{4}$

$\text{Day } = 12\dfrac{3}{4} \text{ hours}$

$\text{Day } = 12 \text{ hours and } 45 \text{ mins}$

Answer: A day is 12 hours 45 mins long and a night is 11 hours 15 mins long