Montreal and Quebec City are about 260km apart along Route 20 in Canada.
Sylvia is leaving Montreal to go to Quebec City at a speed of 90km per hour. And Anne is leaving Quebec City to go to Montreal at a speed of 105km per hour.
a) When and where do Slyvie and Anne pass each other? (Assume that neither one stops along the way. Include a table or a graph with your answer.) Hint: When are they the same distance from Montreal?
b) Write an equation to model this situation. Then show how to solve the equation.
PLEASE! I NEED THIS BADLY!
HELP!
PLEASE!
Ok so just make a table.
Sylvie 90 180 270 360 450 540
--------------------------------
Anne 105 210 315 420 525 630
and so on. Just keep continueing the numbers until you come across the same numbers at the same time.
For the equation it should be 260-90s=260-105.
I'm not sure so you might wan to check with someone else.
are we human?
...
or are we dancers?
(2,3),(9,7)
a) To determine when and where Sylvia and Anne pass each other, we need to find the point where the distances they travel from their respective cities are equal.
Let's start by setting up a table to track the distances each person has traveled based on the time passed:
Time (hours) | Distance traveled by Sylvia (km) | Distance traveled by Anne (km)
------------------------------------------------------------------------------
0 | 0 | 260
To find when they pass each other, we can use the formula Distance = Speed × Time, where Time is in hours.
For Sylvia, the distance traveled is given by: Distance = 90t (where t is the time in hours)
For Anne, the distance traveled is given by: Distance = 105(t - t') (where t' is the time it takes for Anne to reach the point of meeting)
We want to find the time (t) when the distances traveled by both of them are equal. So we set up the equation:
90t = 105(t - t')
Simplifying the equation, we get:
90t = 105t - 105t'
15t = 105t'
t = 7t'
Now we can substitute this value back into one of the equations to find the distance they have each traveled at that time.
For example, substituting t = 7t' into Sylvia's equation:
Distance traveled by Sylvia = 90t = 90(7t') = 630t'
And substituting t = 7t' into Anne's equation:
Distance traveled by Anne = 105(t - t') = 105(7t' - t') = 630t'
At time t = 7t', Sylvia and Anne will have traveled equal distances, 630t' km, from their respective cities. This is when they pass each other.
b) To model this situation with an equation, let's assume t as the time (in hours) when Sylvia and Anne pass each other. The distance traveled by Sylvia at time t is 90t, and the distance traveled by Anne at time t is 105(t - t').
Using the equation Distance = Speed × Time, we can set up the equation:
90t = 105(t - t')
To solve this equation, we can distribute 105 to (t - t'):
90t = 105t - 105t'
90t - 105t = -105t'
-15t = -105t'
t = 7t'
By setting up this equation and finding the value of t, we were able to determine when Sylvia and Anne pass each other.