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.

The key is that they both drove the same time.

let distance driven by Sylvia when they pass each other be x km
then distance driven by Anne would be 260 - x km

Time for Sylvia = x/90
Time for Anne = (260-x)/105

so x/90 = (260-x)/105

cross-multiply and solve for x, then sub the x value into x/90 to find the time

(BTW, totally off topic, I'll be driving to Montreal on Friday)

a) To determine when and where Sylvia and Anne pass each other, we need to find the time at which they are the same distance from Montreal. Let's denote this time as 't'.

Since Sylvia is leaving Montreal at a speed of 90 km per hour, her distance from Montreal can be represented as 90t (her speed multiplied by time).

Similarly, Anne is leaving Quebec City at a speed of 105 km per hour. Since the distance between Montreal and Quebec City is 260 km, Anne's distance from Montreal can be represented as 260 - 105t (initial distance minus her speed multiplied by time).

To find when they pass each other, we set their distances equal to each other and solve for 't':

90t = 260 - 105t

To solve this equation, we can combine like terms:

90t + 105t = 260

195t = 260

Now, divide both sides by 195 to isolate 't':

t = 260 / 195 = 4/3 hours or 1.33 hours

Therefore, Sylvia and Anne pass each other at 1.33 hours, or 1 hour and 20 minutes, after they start their journeys.

To determine where they pass each other, we can substitute the value of 't' back into either of the distance equations. Let's use Sylvia's distance equation:

Distance from Montreal = 90t = 90 * (4/3) = 120 km

This means that they pass each other 120 km from Montreal along Route 20.

We can represent this information in a table as follows:

| Time (hours) | Distance from Montreal (km) |
|--------------|----------------------------|
| 0 | 0 |
| 1.33 | 120 |
| 4/3 | 120 |

b) To model this situation mathematically, we can write the equation by equating the distances of Sylvia and Anne:

90t = 260 - 105t

This equation represents the distance Sylvia has traveled (90t) and the distance Anne has traveled (260 - 105t) being equal.

To solve the equation, combine like terms:

90t + 105t = 260

Combine the coefficients of 't':

195t = 260

Divide both sides by 195:

t = 260 / 195

Simplify the fraction:

t = 4/3 or 1.33 hours.