Math / Numbers & Operations

Question9) Хэвлыийн чехийн ажиттан минутанд $1 \frac{1}{5}$ хуудас уддэг байв. Тэгвэл 60 хуудастай номын хэдэн минутанд үлдэх вэ?

Studdy Solution

STEP 1

1. The worker's typing speed is given as $1 \frac{1}{5}$ pages per minute.
2. This speed can be converted to an improper fraction or a decimal for easier calculations.
3. The goal is to determine the time it takes to type a 60-page book.

STEP 2

1. Convert the typing speed to an improper fraction or decimal.
2. Use the speed to set up an equation relating the number of pages typed to the time taken.
3. Solve for the time required to type 60 pages.

STEP 3

Convert the typing speed $1 \frac{1}{5}$ pages per minute to an improper fraction or decimal.
$1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}$

STEP 4

Alternatively, convert the improper fraction to a decimal.
$\frac{6}{5} = 1.2$

STEP 5

Set up the equation for the number of pages typed in terms of time. Let $t$ be the time in minutes.
$\text{Pages typed} = \text{Typing speed} \times \text{Time}$ $60 = \frac{6}{5} \times t$

STEP 6

Solve for $t$ by isolating $t$ in the equation.
$t = \frac{60}{\frac{6}{5}}$

STEP 7

Simplify the division by multiplying by the reciprocal:
$t = 60 \times \frac{5}{6}$

STEP 8

Calculate the value of $t$ .
$t = 60 \times \frac{5}{6} = 10 \times 5 = 50$

STEP 9

Thus, the time required to type a 60-page book is $50$ minutes.

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Question9) Хэвлыийн чехийн ажиттан минутанд $1 \frac{1}{5}$ хуудас уддэг байв. Тэгвэл 60 хуудастай номын хэдэн минутанд үлдэх вэ?

Studdy Solution

STEP 1

1. The worker's typing speed is given as $1 \frac{1}{5}$ pages per minute.
2. This speed can be converted to an improper fraction or a decimal for easier calculations.
3. The goal is to determine the time it takes to type a 60-page book.

STEP 2

1. Convert the typing speed to an improper fraction or decimal.
2. Use the speed to set up an equation relating the number of pages typed to the time taken.
3. Solve for the time required to type 60 pages.

STEP 3

Convert the typing speed $1 \frac{1}{5}$ pages per minute to an improper fraction or decimal.
$1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}$

STEP 4

Alternatively, convert the improper fraction to a decimal.
$\frac{6}{5} = 1.2$

STEP 5

Set up the equation for the number of pages typed in terms of time. Let $t$ be the time in minutes.
$\text{Pages typed} = \text{Typing speed} \times \text{Time}$ $60 = \frac{6}{5} \times t$

STEP 6

Solve for $t$ by isolating $t$ in the equation.
$t = \frac{60}{\frac{6}{5}}$

STEP 7

Simplify the division by multiplying by the reciprocal:
$t = 60 \times \frac{5}{6}$

STEP 8

Calculate the value of $t$ .
$t = 60 \times \frac{5}{6} = 10 \times 5 = 50$

STEP 9

Thus, the time required to type a 60-page book is $50$ minutes.

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Question9) Хэвлыийн чехийн ажиттан минутанд 1151 \frac{1}{5}151​ хуудас уддэг байв. Тэгвэл 60 хуудастай номын хэдэн минутанд үлдэх вэ?

Studdy Solution

STEP 1

1. The worker's typing speed is given as 1151 \frac{1}{5}151​ pages per minute.2. This speed can be converted to an improper fraction or a decimal for easier calculations.3. The goal is to determine the time it takes to type a 60-page book.

STEP 2

1. Convert the typing speed to an improper fraction or decimal.2. Use the speed to set up an equation relating the number of pages typed to the time taken.3. Solve for the time required to type 60 pages.

STEP 3

Convert the typing speed 1151 \frac{1}{5}151​ pages per minute to an improper fraction or decimal.115=1+15=55+15=65 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} 151​=1+51​=55​+51​=56​

STEP 4

Alternatively, convert the improper fraction to a decimal.65=1.2 \frac{6}{5} = 1.2 56​=1.2

STEP 5

Set up the equation for the number of pages typed in terms of time. Let ttt be the time in minutes.Pages typed=Typing speed×Time \text{Pages typed} = \text{Typing speed} \times \text{Time} Pages typed=Typing speed×Time 60=65×t 60 = \frac{6}{5} \times t 60=56​×t

STEP 6

Solve for ttt by isolating ttt in the equation.t=6065 t = \frac{60}{\frac{6}{5}} t=56​60​

STEP 7

Simplify the division by multiplying by the reciprocal:t=60×56 t = 60 \times \frac{5}{6} t=60×65​

STEP 8

Calculate the value of ttt.t=60×56=10×5=50 t = 60 \times \frac{5}{6} = 10 \times 5 = 50 t=60×65​=10×5=50

STEP 9

Thus, the time required to type a 60-page book is 505050 minutes.

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Question9) Хэвлыийн чехийн ажиттан минутанд $1 \frac{1}{5}$ хуудас уддэг байв. Тэгвэл 60 хуудастай номын хэдэн минутанд үлдэх вэ?

1. The worker's typing speed is given as $1 \frac{1}{5}$ pages per minute.
2. This speed can be converted to an improper fraction or a decimal for easier calculations.
3. The goal is to determine the time it takes to type a 60-page book.

1. Convert the typing speed to an improper fraction or decimal.
2. Use the speed to set up an equation relating the number of pages typed to the time taken.
3. Solve for the time required to type 60 pages.

Convert the typing speed $1 \frac{1}{5}$ pages per minute to an improper fraction or decimal.
$1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}$

Alternatively, convert the improper fraction to a decimal.
$\frac{6}{5} = 1.2$

Set up the equation for the number of pages typed in terms of time. Let $t$ be the time in minutes.
$\text{Pages typed} = \text{Typing speed} \times \text{Time}$ $60 = \frac{6}{5} \times t$

Solve for $t$ by isolating $t$ in the equation.
$t = \frac{60}{\frac{6}{5}}$

Simplify the division by multiplying by the reciprocal:
$t = 60 \times \frac{5}{6}$

Calculate the value of $t$ .
$t = 60 \times \frac{5}{6} = 10 \times 5 = 50$

Thus, the time required to type a 60-page book is $50$ minutes.