MATHEMATICS MIDDLE SCHOOL

Two skaters are racing towards the finish line of the race.the first Skater has a 40 meter lead and is traveling at a rate of 12 meter.the second skater is traveling at a rate of 14 meter per second.how long will it take for the second skater to pass the first skater?

Answers

Answer 1

Answer:

Answer:

20 seconds

Step-by-step explanation:

The distance to cover between the lead skater and trailing skater is 40 meters

The lead skater's rate is 12 m/s

The trailing one's rate is 14 m/s

So, we can say:

second skater is accelerating, or covering up the distance, in 14 - 12 = 2 m/s

So, at a rate of 2 meters per second, how long would it take to cover 40 meters??

We use the distance formula, substitute the known and solve for unknown.

Distance Formula = D = RT

Where

D is distance

R is speed/rate

T is time

We know

r = 2 m/s

d = 40 m

t = ?

Now,

D = RT

40 = 2t

t = 40/2

t = 20 (seconds)

Hence,

it will take 20 seconds for the second skater to catch up (pass)

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Does the equation represent a linear or nonlinear function explain 2x+3y=7

Answers

linear, because there is still a slope function (-2/3)

The equation is linear because you can rewrite it in slope-intercept form.

At a given time of the day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 3 ft stick in the ground casts a shadow is 1.5ft, find the height of a tree that casts a shadow that is 10.15ft

Answers

Answer:

20.3 ft

Step-by-step explanation:

The object-shadow ratio for the stick= 3÷1.5=2:1

The object-shadow ratio is same for all objects.

Let height of the tree be x

2/1 = x/10.15

x=10.15 * 2=20.3

Mr warren drove from Townsville to villaville at 70 mph and back again at a speed of 50 mph. His total driving time was 12 hours. How far apart are the two towns

Answers

Call the distance between the towns 'D' .

The time it takes to cover a distance is (distance) divided by (speed).

It takes Mr. Warren D/70 hours on the first trip,
and it takes him D/50 hours on the return.
All together, it takes him 12 hours.

D/70 + D/50   = 12 hours

Change the fractions to
a common denominator
(350) for adding: 5D / 350 + 7D / 350 = 12

Add: 12D / 350   = 12

Divide each side by 12 :    D / 350   = 1

Multiply each side by 350 : D    = 350 miles .

Check:

Going: 350mi / 70 mph = 5 hours

Coming: 350mi / 50 mph = 7 hours

Total    12 hours    yay !

Warrendrove from Townsville à Villaville at 70 miles per hour
and from Villaville to Townsville è 50 milesper hours
He drove for a total of 12 hours.
=> 70 miles + 50 miles = 120 miles
=> 12 hours
So the unit rate of his driving is 120 miles / 12 hours
=> 120 miles / 12 hours
=> 10 miles / hour
thus, he drove in total for 10 miles per hour.
And probably the 2 towns are about 60 miles away.

Number 6: Which is closer to 0.0009999? 0, 1/2, or 1?

Answers

0.
1/2 is equivalent to 0.5
1 is equivalent to 1.0

How many batches of 12 muffins can be made using one gallon of milk if 1/2 cup of milk makes 12 muffins?

Answers

2, because if you divide one by one half, it equals 2

Final answer:

Given the conversion rate of 1 gallon = 16 cups and that 1/2 cup of milk makes 12 muffins, you can make 32 batches of 12 muffins using one gallon of milk.

Explanation:

The subject we are dealing with here is Mathematics and it's about a practical application of ratios and conversions. The student wants to know how many batches of 12 muffins can be made using one gallon of milk, given that 1/2 cup of milk makes 12 muffins.

To solve this, we first need to understand the relationship between gallons and cups. Specifically, 1 gallon is equivalent to 16 cups. If 1/2 cup of milk makes 12 muffins, hence 1 gallon, or 16 cups, will make 2 batches/cup x 16 cups/gallon = 32 batches of muffins.

Therefore, one gallon of milk can be used to bake 32 batches of 12 muffins each.