Ask question

Ask question

All categories

3 years ago

15

It took Leo 3 hours to type a 4125-word essay. Sarah typed her 3800-word essay in 3 hours and 10 minutes. At these rates, how mu

ch longer would it take Sarah than Leo to type a 5500-word essay?

1 answer:

scoray [572]3 years ago

3 0

Answer:

Sarah would take 35 minutes longer than Leo to type 5500 word essay

Step-by-step explanation:

Let us solve the question

∵ It took Leo 3 hours to type a 4125-word essay

→ The rate is the number of words divided by the time

∴ Leo's rate = 4125 ÷ 3 = 1375 words/hour

∵ Sarah typed her 3800-word essay in 3 hours and 10 minutes

→ Change the 10 min to the hour by divide it by 60

∵ 3 hours 10 min = 3 + $\frac{10}{60}$ = 3 + $\frac{1}{6}$ = 3 $\frac{1}{6}$ hours

∴ Sarah's rate = 3800 ÷ 3 $\frac{1}{6}$ = 1200 words/hour

∵ Leo will type a 5500-word essay

→ Divide it by his rate to find the time taken

∴ Leo takes = 5500 ÷ 1375 = 4 hours

∵ Sarah will type a 5500-word essay

→ Divide it by her rate to find the time taken

∴ Sarah takes = 5500 ÷ 1200 = 4 $\frac{7}{12}$ hours

→ Find the difference between their times

∵ The difference = 4 $\frac{7}{12}$ - 4 = $\frac{7}{12}$ hour

→ Multiply it by 60 to change to minutes

∴ The difference = $\frac{7}{12}$ × 60 = 35 minutes

∴ Sarah would take 35 minutes longer than Leo to type 5500 word essay

You might be interested in

What is the value of the expression StartAbsoluteValue negative 7 EndAbsoluteValue + StartAbsoluteValue negative 4 EndAbsoluteVa

dolphi86 [110]

Answer:

15

Step-by-step explanation: Because the absoulute value of 8 is 8 then the absoultue value of 7 is 7. Then add them together it equals 15 :)

7 0

3 years ago

Read 2 more answers

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago

Please help me fast and show all your work please thx

MrMuchimi

7x4x5= 140
Hope this helps!

7 0

3 years ago

Read 2 more answers

Solve the problem n-6=21

yuradex [85]

Answer:

n=27

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

An angle bisector of a triangle divides the opposite side of the triangle into segments 5 cm and 3 cm long. A second side of the

attashe74 [19]

There is a little-known theorem to solve this problem.

The theorem says that
In a triangle, the angle bisector cuts the opposite side into two segments in the ratio of the respective sides lengths.

See the attached triangles for cases 1 and 2. Let x be the length of the third side.

Case 1:
Segment 5cm is adjacent to the 7.6cm side, then
x/7.6=3/5 => x=7.6*3/5=4.56 cm

Case 2:
Segment 3cm is adjacent to the 7.6 cm side, then
x/7.6=5/3 => x=7.6*5/3=12.67 cm

The theorem can be proved by considering the sine rule on the adjacent triangles ADC and BDC with the common side CD and equal angles ACD and DCB.

6 0

3 years ago