Solved on Feb 06, 2024

Find time difference in hours between Andrew ( $5 \frac{2}{3}$ hours) and Vanessa ( $3 \frac{4}{5}$ hours) taking a test. Express answer in mixed number form.

STEP 1

Assumptions
1. Andrew takes $5 \frac{2}{3}$ hours to take a test.
2. Vanessa takes $3 \frac{4}{5}$ hours to take the same test.
3. We need to find the time difference between Andrew's and Vanessa's test-taking durations.
4. The answer should be expressed in mixed number form and reduced if possible.

STEP 2

First, we need to convert the mixed numbers into improper fractions to make the calculations easier.
For Andrew's time: $5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}$
For Vanessa's time: $3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}$

STEP 3

Now, we will find the difference between the two times by subtracting Vanessa's time from Andrew's time.
$Time\, difference = Andrew's\, time - Vanessa's\, time$

STEP 4

Before subtracting, we need to find a common denominator for the two fractions. The least common denominator (LCD) for 3 and 5 is 15.

STEP 5

Convert both fractions to have the common denominator of 15.
For Andrew's time: $\frac{17}{3} = \frac{17 \times 5}{3 \times 5} = \frac{85}{15}$
For Vanessa's time: $\frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15}$

STEP 6

Now we can subtract Vanessa's time from Andrew's time using the common denominator.
$Time\, difference = \frac{85}{15} - \frac{57}{15}$

STEP 7

Perform the subtraction.
$Time\, difference = \frac{85 - 57}{15}$

STEP 8

Calculate the difference.
$Time\, difference = \frac{28}{15}$

STEP 9

Since the numerator is larger than the denominator, we can convert the improper fraction back into a mixed number.
$Time\, difference = 1 \frac{13}{15}$

STEP 10

The fraction $\frac{13}{15}$ is already in its simplest form, so no further reduction is necessary.
The time difference between Andrew's and Vanessa's test-taking durations is $1 \frac{13}{15}$ hours.

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Find time difference in hours between Andrew ( $5 \frac{2}{3}$ hours) and Vanessa ( $3 \frac{4}{5}$ hours) taking a test. Express answer in mixed number form.

STEP 1

Assumptions
1. Andrew takes $5 \frac{2}{3}$ hours to take a test.
2. Vanessa takes $3 \frac{4}{5}$ hours to take the same test.
3. We need to find the time difference between Andrew's and Vanessa's test-taking durations.
4. The answer should be expressed in mixed number form and reduced if possible.

STEP 2

First, we need to convert the mixed numbers into improper fractions to make the calculations easier.
For Andrew's time: $5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}$
For Vanessa's time: $3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}$

STEP 3

Now, we will find the difference between the two times by subtracting Vanessa's time from Andrew's time.
$Time\, difference = Andrew's\, time - Vanessa's\, time$

STEP 4

Before subtracting, we need to find a common denominator for the two fractions. The least common denominator (LCD) for 3 and 5 is 15.

STEP 5

Convert both fractions to have the common denominator of 15.
For Andrew's time: $\frac{17}{3} = \frac{17 \times 5}{3 \times 5} = \frac{85}{15}$
For Vanessa's time: $\frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15}$

STEP 6

Now we can subtract Vanessa's time from Andrew's time using the common denominator.
$Time\, difference = \frac{85}{15} - \frac{57}{15}$

STEP 7

Perform the subtraction.
$Time\, difference = \frac{85 - 57}{15}$

STEP 8

Calculate the difference.
$Time\, difference = \frac{28}{15}$

STEP 9

Since the numerator is larger than the denominator, we can convert the improper fraction back into a mixed number.
$Time\, difference = 1 \frac{13}{15}$

STEP 10

The fraction $\frac{13}{15}$ is already in its simplest form, so no further reduction is necessary.
The time difference between Andrew's and Vanessa's test-taking durations is $1 \frac{13}{15}$ hours.

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Find time difference in hours between Andrew (5235 \frac{2}{3}532​ hours) and Vanessa (3453 \frac{4}{5}354​ hours) taking a test. Express answer in mixed number form.

STEP 1

STEP 2

STEP 3

Now, we will find the difference between the two times by subtracting Vanessa's time from Andrew's time.Time difference=Andrew′s time−Vanessa′s timeTime\, difference = Andrew's\, time - Vanessa's\, timeTimedifference=Andrew′stime−Vanessa′stime

STEP 4

Before subtracting, we need to find a common denominator for the two fractions. The least common denominator (LCD) for 3 and 5 is 15.

STEP 5

STEP 6

Now we can subtract Vanessa's time from Andrew's time using the common denominator.Time difference=8515−5715Time\, difference = \frac{85}{15} - \frac{57}{15}Timedifference=1585​−1557​

STEP 7

Perform the subtraction.Time difference=85−5715Time\, difference = \frac{85 - 57}{15}Timedifference=1585−57​

STEP 8

Calculate the difference.Time difference=2815Time\, difference = \frac{28}{15}Timedifference=1528​

STEP 9

Since the numerator is larger than the denominator, we can convert the improper fraction back into a mixed number.Time difference=11315Time\, difference = 1 \frac{13}{15}Timedifference=11513​

STEP 10

The fraction 1315\frac{13}{15}1513​ is already in its simplest form, so no further reduction is necessary.The time difference between Andrew's and Vanessa's test-taking durations is 113151 \frac{13}{15}11513​ hours.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find time difference in hours between Andrew ( $5 \frac{2}{3}$ hours) and Vanessa ( $3 \frac{4}{5}$ hours) taking a test. Express answer in mixed number form.

Now, we will find the difference between the two times by subtracting Vanessa's time from Andrew's time.
$Time\, difference = Andrew's\, time - Vanessa's\, time$

Now we can subtract Vanessa's time from Andrew's time using the common denominator.
$Time\, difference = \frac{85}{15} - \frac{57}{15}$

Perform the subtraction.
$Time\, difference = \frac{85 - 57}{15}$

Calculate the difference.
$Time\, difference = \frac{28}{15}$

Since the numerator is larger than the denominator, we can convert the improper fraction back into a mixed number.
$Time\, difference = 1 \frac{13}{15}$

The fraction $\frac{13}{15}$ is already in its simplest form, so no further reduction is necessary.
The time difference between Andrew's and Vanessa's test-taking durations is $1 \frac{13}{15}$ hours.