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Lubov Fominskaja [6]
3 years ago
12

Dave can complete a sales route by himself in 4 hours. James can do the same job in 5 hours. How long will it take them to do it

working together?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
3 0
We can solve this problem by calculating the individual rate of working and equate it to their total rate of working.

If Dave can complete a sales route in 4 hours, then his working rate is

\frac{1}{4}

Also, if James can do it in 5 hours, then his working rate is

\frac{1}{5}

Let
x
be the hours that both will use to complete the sales route,

Then rate at which both completes this task is
\frac{1}{x}


Meaning if we add their individual rates we should get

\frac{1}{x}

That is;

\frac{1}{4} + \frac{1}{5} = \frac{1}{x}

The LCM is
20x

So let us multiply through with the LCM.

20x \times \frac{1}{4} + 20x \times \frac{1}{5} =20x \times \frac{1}{x}

5x + 4x = 20

We simplify to get,

9x = 20

Dividing through by 9 gives;

x = \frac{20}{9}

x = 2\frac{1}{9}

Therefore the two will complete sales route in
2 \frac{1}{9}
hours.
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You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate
DanielleElmas [232]

It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

A=P(1+\frac{r}{n})^{nt} , where

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount  
  • r is the annual interest rate (decimal)
  • n is the number of times that interest is compounded per unit t
  • t is the time the money is invested or borrowed for

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

   compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ 3000=2000(1+\frac{0.04}{12})^{12t}

- Divide both sides by 2000

∴ 1.5=(1+\frac{1}{300})^{12t}

∴ 1.5=(1\frac{1}{300})^{12t}

- Change the mixed number to an improper fraction

∴ (1.5)=(\frac{301}{300})^{12t}

- Insert ㏒ for both sides

∴ log(1.5)=log(\frac{301}{300})^{12t}

- Remember log(a)^{n}=nlog(a)

∴ log(1.5)=(12t)log(\frac{301}{300})

- Divide both sides by log(\frac{301}{300})

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

Learn more:

You can learn more about the compound interest in brainly.com/question/4361464

#LearnwithBrainly

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