Hi, there-- THE PROBLEM: Two cars are leaving at the same time from two diffirent provinces which are 150 km apart. If car A travels at 5 kph faster than car B, find their rates if they meet after two hours. A SOLUTION: We need to use the big idea that [Rate] * [Time] = [Distance]. We also assume that the cars are traveling straight towards each other. Furthermore, each car travels at a constant speed. We want to find the rate of each car. Define variables and expressions: Let r be the rate of the car A (in km/hr). Then the rate of car B will be r-5 because Car A is driving faster. We know the cars are 150 km apart at the start. We know that the cars will meet somewhere in the middle. It won't be exactly in the middle, though, because car A is driving faster and can cover more territory in 2 hours. We can say that their combined distance traveled is 150 km. Do you see why that is? We need to write an expression for the distance each car travels and then write an equation showing the sum of the distance to be 150 km. Car A: Car A travels at a rate of r km/hr. It travels for 2 hours until the two drivers meet. [Rate] * [Time] = [Distance] so an expression for car B's distance is r*2, or 2r. Car B: [Rate} * [Time] = [Distance] so an expression for car B's distance is (r-5)*2, or 2(r-5). Now our equation is [Car A's distance] + [car B's distance] = [150 km] Substitute each expression into the equation and we haveSimplify and solve for r. In the context of this problem, r=40 means that car A's rate is 40 km/hr. Since car B is traveling 5 km/hr slower than car A, car B's rate is 40-5=35 km/hr. Let's check our work against the words in the original problem. "Car A is traveling 5 kph faster than Car B." We see that 40 kph is 5 kph faster. CHECK! "The cars are...150 km apart…they meet after two hours." In 2 hours, Car A travels 80 km (40 km for each hour.) In 2 hours, Car B travels 70 km (35 km for each hour.) They started 150 km apart and headed toward each other. When they met after 2 hours, they had covered 80+70=150 km. CHECK! Hope this helps! Mrs. Figgy math.in.the.vortex@gmail.com