Rick took a 45-minute lunch break. At the end of the break, it was 1:00 P.M. What time did Rick start his lunch break?

Solving 8 problems per minute, Fast Finn can finish his test in time. He was however, working faster, solving 10 problems per mi

mrs_skeptik [129]

Answer:

Number of problems = 240

Step-by-step explanation:

Let x be the number of questions and t be the time.

Given:

Average rate = 8 problems per minute

Fast Finn rate = 10 problems per minute

Fast Finn taken time = t - 6

We need to find the number of problems on the test paper.

Solution:

Average rate to solve test paper.

$Average\ rate =\frac{Number\ of\ questions}{time}$

$8 =\frac{x}{t}$

$t =\frac{x}{8}$ --------------(1)

Fast Finn rate to solve the test paper.

$Average\ rate =\frac{Number\ of\ questions}{time}$

$10 =\frac{x}{t-6}$

Using cross multiplication rule.

$x=10(t-6)$

$x=10t-60$

substitute $t =\frac{x}{8}$ from equation 1.

$x=10(\frac{x}{8}) -60$

Rearrange the equation as:

$x - \frac{5}{4}x = -60$

$\frac{4x-5x}{4}=-60$

$-\frac{x}{4} = -60$

Using cross multiplication rule.

$x = 60\times 4$

x = 240 problems.

Therefore, 240 problems were on the test.

4 0

4 years ago

3/5×2/7×2/3 Please fallow

olga55 [171]

Answer:

$\frac{12}{105}$

Step-by-step explanation:

$\frac{3}{5}x\frac{2}{7}x\frac{2}{3}$

3x2x2=12

5x7x3=105

$\frac{12}{105}$

6 0

3 years ago

Hilda was simplifying some numerical expressions and made each of the following sequences of calculations. Name the mathematical

Galina-37 [17]

Answer:

Problem 1:

5 · (−4/3) · (2/5)

= (−4/3) · 5 · (2/5) Conmutative Property of Multiplication

= (−4/3) · (5 · (2/5)) Associative Property of Multiplication

= (−4/3) · (2/1) = −8/3 = −2*2/3 Multiplied fractions and extracted common factor

Problem 2:

17 + 29 + 3+ 1

= 17 + 3 + 29 + 1 Conmutative Property of Addition

= (17 + 3) + (29 + 1) Associative Property of Addition

= 20 + 30 Added groups

= 50 Added terms

Step-by-step explanation:

For the Problem 1:

In the first step, Hilda applied the Conmutative Property of Multiplication, because she changed the order of the numbers in the product

In the second step, she applied the Associative Property of Multiplication, because she agrouped the product of 5 and 2/5 to perform it sepparately

In the third step, she calculated the product of the fractions -4/3 and 2/1, then she extracted 2 as a common factor to express the fraction as -2*2/3

For the Problem 2:

In the first step, Hilda applied the Conmutative Property of Addition, because she changed the order of the numbers in the sum

In the second step, she applied the Associative Property of Addition, because she associated the addition of 17 and 3 and the addition of 29 and 1, to calculate them in groups.

4 0

3 years ago

Read 2 more answers

Write each ratio as a fraction in lowest terms. 8 to 9

3241004551 [841]

Answer:

8/17 and 9/17

Step-by-step explanation:

8:9

both add up to 17

so it can be 8/17 or 9 but it cannot be simplified unless if you want them both as a mixed number which is

8/17 as a mixed number is 2 1/17

9/17 as a mixed number is 1 8/17

8 0

3 years ago

Y is greater than or equal to -×-5

Katen [24]

Answer:

Y>-x-5

Step-by-step explanation:

6 0

4 years ago