Answer #1: We think it takes Jack 5 minutes per lap, and Jill 9 minutes per lap.

Explanation: Considering that it takes the same amount of time for Jack and Jill to do a different number of units (Jack doing 9 units and Jill doing 5 units), the amount of time must be divisable by both 5 and 9. SO, the easiest way to do this is to find the least common multiple, 45. This means it takes them 45 minutes to do their personal number of units.

If you divide 45 minutes by the # of units, you got the amount of time it takes them to do one unit.

45 / h = m

45 / 9 (units) = 5 (minutes per unit) ----Jack
45 / 5 (units) = 9 (minutes per unit) ----Jill
Now that you've got the amount of time it takes them, all you have to do is find the miles per hour. To do this, you divide the amount of time it takes each person to do one unit and divide that number into 60, because there are 60 minutes in an hour, and you ARE trying to find the miles per HOUR. When you do that you get.....

60 / m = mph

60 / 5 (Jack's total minutes per unit) = 12 mph

Next, it says that if Jill goes 3 miles per hour faster, she will go as fast as Jack does. All you have to do is subtract 3 miles per hour from Jack's 12 mph.

mph - 3 = j

12 - 3 = 9 Miles per hour.

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Answer #2: We found that jack can run 3 units per hour and Jill can run 1.7 untits per hour if she runs under normal circumsatances.

Explanation: Since Jill can run 3 units per hour if or the same as Jack if she increases her speed, then you know that Jack can run three units per hour under normal circumstances. first you would do 9 divided by 3 to get Jacks speed. You do the same for Jill, 5 divided by 3=units per hour. The solution is 1.7 units/hour for Jill and 3 units/hour for Jack.

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Answer#3: one runs in miles the other in meters

Explanation: thats the only way becauce 5+3=8. i knew i was dealing with different units

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Answer #4: Jack and Jill can each jog 3.75 units per hour.

Explanation: (m) = jack's distance of jogging in units for however long the time period is (m also for masculine)
(f) = jill's distance of jogging in units for however long the time time period is (f also for feminine)
(t) = however long they were jogging (time)

Distance = rate multiplied by time (D=rt)
Rate = distance divided by time (r=d divided t)

****Whenever I put the slash symbol in it doesn't mean a fraction it means (a) over 3 -       or     - 7 over (z)****
9/m = mt/m    5/f = ft/f   9 is how far jack can jog.
9m = t    5f = t    5 is how far jill can jog.

9/m = 5/f
m = f+3

9/f+3 = 5/f
But since we are trying to figure out how fast they can jog we need to flip around the equation because rate equals distance divided by time.

f+3/9 = f/5
use the distributive property
5f + 15 = 9f
-5f   -5f
15 = 4f
15/4 = 4f/4
f = 3.75 units

I HOPE THAT ANSWER IS RIGHT!!!! PLEASE O PLEASE!!!!

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Answer #5: Under normal circumstances, Jack can jog 12 units per hour and Jill can jog 6 2/3 units per hour. In 1 1/2 hours, Jack can jog 18 units, and Jill can jog 10 units.

Explanation: Jack jogs 9 units in the same time Jill jogs 5 units.

We will use x to represent the number of hours they were jogging. If Jill can increase her speed by 3 units per hour, they could cover the same distance.

So thus we have:

9x = 5x + 3

which can be simplified by subtracting 5x from both sides:

9x - 5x = 5x - 5x + 3

4x = 3

x = 3/4

In 3/4 of an hour, Jack covered 9 units and Jill covered 5 units.

I find how far each jogs in an hour by multiplying how far they each went (in 3/4 of an hour) by 4/3. I used 4/3 because 3/4 of an hour times 4/3 equals one full hour.

9 X 4/3 = 12
5 X 4/3 = 6 2/3

In one hour, Jack jogged 12 units, and Jill jogged 6 2/3 units.

Jack jogs at a speed of 12 units per hour and Jill jogs at a speed of 6 2/3 units per hour.

To find how far each will jog in 1 1/2 hours, I multiply their distance covered in one hour by 1 1/2.

12 X 1 1/2 = 18
6 2/3 X 1 1/2 = 10

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Answer#6: Jill can jog 4.2 units per hour
Jack can jog 8.2 units per hour

Explanation: Let the variable T equal time
5t=9t
5x3t=9t
5=6t
t=1.2

1.2 plus three because she increases her speed by 3 units per hour equals 4.2

Then to get Jack's number 4.2 plus four because Jack jogs four units faster equals 8.2

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