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3 years ago

1

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

6 0

Answer:

Fraction of the original board left = $\frac{2}{15}$

Step-by-step explanation:

Let the length of the board is = l feet

Marty saws off $\frac{1}{5}$ of a wooden board.

Length of the board left = l - $(\frac{1}{5})l$

= $(\frac{4}{5})l$ feet

He saws off $\frac{3}{4}th$ of the remaining board,

Board left = $(\frac{4}{5})l-[(\frac{4}{5})l\times (\frac{3}{4})]$

= $\frac{4}{5}l-\frac{3}{5}l$

= $\frac{1}{5}l$ feet

He finally saws off $\frac{1}{3}$ rd of the remaining board.

Board left = $\frac{1}{5}l-[\frac{1}{5}\times \frac{1}{3}]l$

= $(\frac{1}{5}-\frac{1}{15})l$

= $\frac{2}{15}l$ feet

Fraction of the original board left = $\frac{\frac{2}{15}l}{l}$

= $\frac{2}{15}$

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The distance Train A travels is represented by d = 67t, where d is the distance in kilometers and t is the time in hours. The di

Thepotemich [5.8K]

Answer:

Train A's unit rate is 67 km per hour.

Train B's unit rate is 75 km per hour.

Train B is faster than Train A

Step-by-step explanation:

Train A

Distance traveled by Train A is represented by :

$d=67t$

where $d$ represents distance traveled in kilometers and $t$ is the time in hours.

To find the unit rate of Train A, we will plugin $t=1$ and get the distance traveled by Train A in 1 hour which will be the unit rate of Train A in km/hr.

$d=67(1)$

$d=67$

So, distance traveled by Train A in 1 hour = 67 km

∴ Train A's unit rate is 67 km per hour.

Train B

For Train B, we are given the table for the time in hours and distance traveled in that duration.

Taking time =2 hours the distance traveled by Train B= 75 km

To find distance traveled in 1 hour we apply unitary method.

$2\ hr = 150\ km$

So $1\ hr = \frac{150}{2}\ km = 75\ km$

So, distance traveled by Train B in 1 hour = 75 km

∴ Train B's unit rate is 75 km per hour.

Difference in units rates = $75-67=8\ km/hr$

On comparing their unit rate i.e. the speed of the trains we find out that Train B is faster than Train A by 8 km/hr

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4 years ago

What volume of fluid does a patient receive in 12 hours with a fluid rate of 24 mL/hr?

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

2(2x - 4) = 4(x - 2)<br> What is the solution

galben [10]

Answer: 0

Step-by-step explanation:

2(2x-4)=4(x-2) - Start off by diong distributive property on both sides

4x-8=4x-8 - Add 8 to both sides toget rid of it

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Hope this helps!

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3 years ago

Matt and Anna Killian are frequent fliers on Fast-n-Go Airlines. They often fly between two cities that are a distance of 1680

vladimir1956 [14]

Answer:Wind speed = 30 miles/hour

Plane speed = 450 miles/hour

Step-by-step explanation:

First we have to know the formula for finding speed, which is distance divided by time

Speed = distance/time

Then we label the speed of the plane to be x

And the spend of the wind to be y

From the question, we are told that when the plane flies into the wind, it takes 4 hours to travel a distance of 1680 so we have the time and distance

And since the plane is flying against the wind speed

We can form an equation

x - y = 1680/4

x - y = 420 (1)

Then when the plane is coming back, the wind is going in the same direction with the plane and it take 3.5 hours to cover the same 1680 miles distance, so we form another equation

x + y = 1680/3.5

x + y = 480 (2)

So we solve (1) and (2) simultaneously

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x + y = 480 (2)

Using elimination method, we eliminate y by adding both equations

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So therefore, plane speed is 450 miles/hour

Putting the answer in either (1) or (2) to get y

I choose to put it in (2)

x + y = 480

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y = 480 - 450

y = 30 miles/hour

So therefore, wind speed = 30miles/hour

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3 years ago

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kirza4 [7]

Answer:

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and for the second one

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