We'll be looking for time here.
s=d/t
ts=d
t=d/s
------------------------
Average speed is:
s=(55m)/h
Distance is:
200m
---------------------------
t=(200m)/(55m/h)
t=(200m/1)*(h/(55m))
t=200/55*h
t≈3.64 hours
Answer: they are both the same fraction
You would simply add the last two equations together. If v=2x+1 and t=4x-1, you can add them up. This would make 2x+1+4x-1. If you combine like terms, 1 and -1 cancel out and you are left with 6x. This means x can be anything.
Question 1 Answer:
Aunt 1 and Grandma 1 would fill gift bags.
Mom and Aunt 2 would make centerpieces.
You and Grandma 2 would blow up balloons.
Since you are pairing up to complete the tasks, these pairs each have the shortest times in their respective categories and therefore are the most logical pairing to complete tasks.
Question 2 Answer:
We use algebra and our previous pairings to determine the length of each task.
<u>Gifts Bags --> 6/7 hours</u>
x = time together
= rate of completion
Aunt 1 = 
Grandma 1 = 
<u>Centerpieces --> 7/4 hours</u>
x = time together = rate of completion
Mom = 
Aunt 2 =
<u>Balloons --> 15/16 hours</u>
x = time together = rate of completion
You = Grandma 2 = 
Shortest amount of time to complete all tasks is:
≈ 3.54 hours
Converting hours to hours and minutes --> 3 hours 32 minutes
Therefore they must arrive by 5:28pm to complete the tasks in time to leave at 9:00pm.
Answer:
7
Step-by-step explanation:
We want to find the number 4-digit of positive integers n such that removing the thousands digit divides the number by 9.
__
Let the thousands digit be 'd'. Then we want to find the integer solutions to ...
n -1000d = n/9
n -n/9 = 1000d . . . . . . add 1000d -n/9
8n = 9000d . . . . . . . . multiply by 9
n = 1125d . . . . . . . . . divide by 8
The values of d that will give a suitable 4-digit value of n are 1 through 7.
When d=8, n is 9000. Removing the 9 gives 0, not 1000.
When d=9, n is 10125, not a 4-digit number.
There are 7 4-digit numbers such that removing the thousands digit gives 1/9 of the number.
