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A father and his son can clean the house together in 9 hours. When the son works alone, it takes him an hour longer to clean th

leonid [27]

Answer:

It will take the son 18.55 hours

Step-by-step explanation:

It takes 9 hours for the father and son to clean the house if they work together. This means that their unit rate of working together will be 1/9

When the son works alone, it takes him an hour longer to clean than it takes his dad alone.

Let x = the time it takes the father to clean the house. This means that it takes the son (x+1) hours to clean the house alone.

The unit rate if working of the son will be 1/+1

The unit rate of working of the father will be 1/x

Since they are working simultaneously, their unit rates are additive. Therefore

1/(x+1) + 1/x = 1/9

(x + x + 1)/x(x+1) = 1/9

(2x+1)/(x^2 + x)= 1/9

18x + 9 = x^2 + x

x^2 + x - 18x-9

x°2 - 17x - 9 = 0

Applying the general formula for quadratic equations,

x = [-b+-√b^2-4ac)]/2a

x =[ - -17 +-√-17^2-4(2×1)]/2×1

x = (17+-18.03)/2

x = (17 + 18.03)/2 or x = (17 - 18.03)/2

x = 17.55 or x = -0.515.

The time cannot be negative so it is 17.55

It takes the father 17.55 hours if he works alone.

It will take the son 17.55 + 1 = 18.55 hours

4 0

3 years ago

Rove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero.

liubo4ka [24]

Answer:

$\frac{ad+bc}{bd}$

Step-by-step explanation:

$Greetings!$

$I'm~Isabelle~Williams~and~I~will~be~answering~your~question!$

$Let,\frac{a}{b} ~and ~\frac{c}{d}~be~two~rational~numbers, ~where~ b ~and~ d ~are~ not~ zero ~and~ a, ~b, ~c ~and \\~d ~are~ integers.$

$1.~Given:$

$\frac{a}{b} +\frac{c}{d}$

$2.~Now,~we~multiply~to~get~a~common~denominator:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}$

$3.~Then~simplify:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}=\frac{ad+bc}{bd}$

$4.~Since,b\neq 0,~d\neq 0,~then,~bd,~ad,~bc~and~ad+bc~are~integers~too.~So~the\\ fraction~will~be:$

$\frac{ad+bc}{bd}$

$Thus,~making~it~a~rational~number!$

$Hope~this~answer~helps!~and~have~an~amazing~day~ahead!$

$-Isabelle~Williams$

8 0

3 years ago

Read 2 more answers

A wholesale dealer offers 8 lamps for a price of p dollars. Which expression represents the price of a single lamp? A. 8p B. p+8

Nostrana [21]

Find the "unit cost." Divide the total price paid by the number of units sold:

$p
------------ = $(p/8) / lamp
8 lamps

The unit cost is p/8 dollars per lamp.

5 0

4 years ago

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The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of

Sati [7]

Answer:

<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>

Step-by-step explanation:

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

b - base

h - height

We have b = 21cm, h = 6cm.

Substitute:

$A=\dfrac{(21)(6)}{2}=63\ cm^2$

The formula of an area of a trapezoid:

$A=\dfrac{b_1+b_2}{2}\cdot h$

b₁, b₂ - bases

h - height

We have b₁ = 2b₂, therefore b₁ + b₂ = 2b₂ + b₂ = 3b₂.

The area of a triangle and the area of a trapezoid are the same.

Therefore

$\dfrac{3b_2}{2}\cdot h=63$ multiply both sides by 2

$3b_2h=126$ divide both sides by 3

$b_2h=42$ divide both sides by h

$b_2=\dfrac{42}{h}$

$b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}$

8 0

3 years ago

Read 2 more answers

Which equation has infinitely many solutions?

SpyIntel [72]

The answer is b the second one

5 0

3 years ago