MATHEMATICS MIDDLE SCHOOL

Jack and Jill live 345 miles apart from one another. They want to meet for lunch and agree to leave thesame time, drive toward each other, and meet somewhere along the route. lack's average rates 60 pland
Hill's average rate is 55mph How long will it take them to meet? Give your wet in bo and sites

Answers

Answer 1
Answer:

It will take them 3 hours to meet

Step-by-step explanation:

The given is:

  • Jack and Jill live 345 miles apart from one another
  • They want to meet for lunch and agree to leave the  same time, drive toward each other, and meet somewhere along the route
  • Jack's average rates 60 mph
  • Jill's average rate is 55 mph

We need to find how long it will take them to meet

Distance = Speed × Time

∵ They will drive toward each other at the same time and meet

   each other somewhere

- That means they will drive for the same time

∵ Jack's average rates 60 mph for t hours

∴ Jack will drive a distance = 60 × t = 60 t  miles

∵ Jill's average rate is 55 mph for t hours

∴ Jill will drive a distance = 55 × t = 55 t  miles

∵ The distance between Jack and Jill is 345 miles apart

- Add their distance above and equate the sum by 345

∴ 60 t + 55 t = 345

∴ 115 t = 345

- Divide both sides by 115

∴ t = 3 hours

It will take them 3 hours to meet

Learn more:

You can learn more about the word problems in brainly.com/question/3950386

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A flagpole casts a shadow that is 26 ft long. At the same time, a yardstick casts a shadow that is 4 ft long. How tall is the flagpole?

Emily and Sarah had a total of $80. After Sarah spent 1/3 of her money and Emily spent $17, Emily had twice as much money as Sarah. How much more money did Emily have than Sarah at first?

Answers

Emily = E
Sarah = S

At the end

E = 2S (Because Emily has double Sarah)
E -> E + 17 (To make up the $17 she spent)
2S -> 3S (Because 2S is two thirds the amount Sarah had, as she spent a third)
E + 17 + 3S = 80 (Because their original amounts were equal to $80)
E + 3S = 63 (Simplifying equation)

I think Emily had 3x as much as Sarah 

What is the value of x, when -9(x-5)=x+22 1/2​

Answers

Answer:

\large\boxed{x=(9)/(4)=2(1)/(4)}

Step-by-step explanation:

-9(x-5)=x+22(1)/(2)\qquad\text{multiply both sides by 2}\n\n(2)(-9)(x-5)=2x+(2)\left(22(1)/(2)\right)\n\n-18(x-5)=2x+45\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\n\n(-18)(x)+(-18)(-5)=2x+45\n\n-18x+90=2x+45\qquad\text{subtract 90 from both sides}\n\n-18x+90-90=2x+45-90\n\n-18x=2x-45\qquad\text{subtract}\ 2x\ \text{from both sides}\n\n-18x-2x=2x-2x-45\n\n-20x=-45\qquad\text{divide both sides by (-20)}\n\n(-20x)/(-20)=(-45)/(-20)\n\nx=(45:5)/(20:5)\n\nx=(9)/(4)\to x=2(1)/(4)

Answer:

x = 2.25

Step-by-step explanation:

 -9(x - 5) = x + 22 1/2

Distribute the nine and then add 9x to both sides

 -9x + 45 = x +22 1/2

+ 9x        + 9x

Then try to get x alone

       45 = 10x + 22 1/2

     -22 1/2       -22 1/2

    22.5 = 10x

   (22.5)/(10) = (10x)/(10)

   2.25 = x

I only need number 16.

Answers

4(x - 2) is different from the others, due to the distributive property of multiplication. All of the other options can be simplified into (or already are) 4x - 2. 4(x - 2), however, would simplify into 4x - 8. So 4(x - 2) is your answer.
4(x-2) are not equivalent to other three.
It has the value of 4x-8 which is different from other three.
The value of other three expression is 4x-2.

What is the least common multiple of 36 and 200

Answers

The least common multiple (LCM) of 36 and 200 is: 1800

36 × 50 = 1800
200 × 9 = 1800

Katherine and Shelly had $288 altogether. Katherinine gave 1/3 of her share to Shally and their father gave $68 to Shally. They now have the sme amount ofMoney. How
Much money did
Shally have at first?

Answers

This is a problem that has to be read minutely to understand the tricks inside it.
Amount of money Catherine and Shelly had altogether = $288
Now Katherine gave 1/3 of her share to Shelly.
Let us assume the amount of money Katherine had = x
Amount of money Katherine gives to Shelly = x/3
The amount of money given by their father to Shelly = $68
Then
Amount of money that Katherine now has = [(x/3) + 68]
Now we can easily get to the equation
x = [(x/3) + 68]
3x = x + (68 * 3)
3x - x = 204
2x = 204
x = 204/2
  = 102
So the amount of money that Katherine has = $102
Amount of money Shelly had at first = x/3
                                                         = 102/3 dollars
                                                         = 34 dollars
So Shelly at first had $34 with her.

I'm curious as to how a wrong answer can be a "verified answer." What is BRAINLY's  process for verification?

You can see an error in the "verified answer" here:

"Amount of money that Katherine now has = [(x/3) + 68]"

No. If X is the amount of money Katherine had, and she gave away 1/3, then she has 2/3(x). And the +68?

Shelly's dad gave that $68 to Shelly, not to Katherine.

The answer my son and I came up with was $21. We used bar models since they aren't teaching 2-variable algebra in 5th grade. But here's the logic.

We know what Katherine and Shelly collectively now have $356 ($288 + $68 from the dad).

They have equal amounts now, so they each have $178. Half of that is $89, which is significant since we need to find the value of the "thirds" that constitute Katherine's original amount. She has two of those thirds left and each of the two is worth $89 (half of what she has now). This is really where the bar model method helps to visualize, by the way.

Now we now how much Katherine gave Shelly: $89 (same value as each of the other two, equal thirds of Katherine's original amount).

If we know that the $178 Shelly has now is made up from the $89 that Katherine gave her, plus the $68 her dad gave her, plus whatever mystery amount she started with, we can do $178 - ($68 + $89) and get $21.


Let's verify this answer right here:

Katherine started with $267 and Shelly started with $21.

Katherine gave Shelly $89 (1/3) of her money.

Katherine now has $178 ($267 - $89) and Shelly now has $110 ($21 + $89).

Shelly's dad gave her another $68. Now they both have $178.

X(x+9)=0
x=?
What does x have to be for the answer to be 0?

Answers

when we solve the equation it will become
x² + 9x= 0
now here a = 1 , b = 9 and c = 0 
by using quaderatic formula
x = -b +,-√b ²- 4ac / 2a     ( 2a is divided by all terms )
by putting values
x = - 9 +,- √81 / 2(1)               ( √81 = 9)
x = -9 + 9 / 2    and x = -9 -9 /2
x = 0                and x = -18 /2 = -9  
now there are two values for x one is- 9 and other is 0 
so we put -9 as the value of x then answer will be zero..
x(x+9)=0\nx=0 \vee x=-9
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