Answer item 2 Example: Two pipes are used to fill a water storage tank. The first pipe can fill the tankin four hours. The two pipes together can fill the tank in 2 hours less time than thesecond pipe alone. How long would it take for the second pipe to fill the tank?Step 1. Representation of the unknownLet x = required time for the second pipe to fill the tank.!= rate of the first piperate of the second piperate of two pipes togetherStep 2 Working Equation: Rate of the 1" pipe plus rate of the 20d pipe equals rate of two pipestogether.r-2Step 3. Solve for x4x(x - 2)+=4x(x-2) Clear the equationx(x – 2) + 4(x – 2) = 4x- apply distributive property to simplify- Factor the quadratic expression- Equate each factor to zerox2 – 2x + 4x –8- 4x 0x2 - 2x – 8 = 0(x – 4)(x + 2) = 0x - 4 = 0, x+ 2 = 0- Solve for xx = 4, x = -2Answer: Therefore, it takes 4 hours for the second pipe to fill the tank.TRY: Solve the following Equations2. A motorist travels for 20km at one speed, and then increased her speed by 20 kphfor next 30 km. How fast was she traveling originally if the total trip took 1 hour? APPLICATION OF QUADRATIC EQUATIONSMOTION PROBLEMS / WORK PROBLEMSMotion Problem: Distance = Rate x TimeFormula to be used in solvingWork Problem: Work = Rate x Timethese type of worded problemsExample: A car travels 10kph faster than a truck. The car goes 600 km in 5 hours less time thanit takes the truck to travel the same distance. Find the rate of each vehicle in kilometers perhour.dStep 1. Representation of the unknownCar600x+ 10600Let x = rate of the truckx+ 10x + 10 = rate of the carTruck600600Step 2. Working Equation: (Time spent by truck traveling 600 km) minus (time spent by cartraveling 600 km) is 5600600= 5x+10Step 3. Solve for x[600600x(x + 10)5 (x+10)(x) clear the equationx+10- combine similar term- reduce the equation by dividing each term by 5- Factor the quadratic expression- equate each factor to zero.600x + 6000 – 600x = 5x2 + 50x5x? + 50x – 6000 = 0x2 + 10x - 1200 = 0(x + 40)(x – 30) = 0x + 40 = 0,x –- 30 = 0- solve for xx = -40, x = 30Note: -40 can not be rate of the car because when it comes to the rate should be positive, sothe rate of the car is 30 kph.Answer: Therefore, the rate of the car is 30 kph and the rate of the truck is 40Okph.

Question

Answer item 2 Example: Two pipes are used to fill a water storage tank. The first pipe can fill the tankin four hours. The two pipes together can fill the tank in 2 hours less time than thesecond pipe alone. How long would it take for the second pipe to fill the tank?Step 1. Representation of the unknownLet x = required time for the second pipe to fill the tank.!= rate of the first piperate of the second piperate of two pipes togetherStep 2 Working Equation: Rate of the 1&#34; pipe plus rate of the 20d pipe equals rate of two pipestogether.r-2Step 3. Solve for x4x(x - 2)+=4x(x-2) Clear the equationx(x – 2) + 4(x – 2) = 4x- apply distributive property to simplify- Factor the quadratic expression- Equate each factor to zerox2 – 2x + 4x –8- 4x 0x2 - 2x – 8 = 0(x – 4)(x + 2) = 0x - 4 = 0, x+ 2 = 0- Solve for xx = 4, x = -2Answer: Therefore, it takes 4 hours for the second pipe to fill the tank.TRY: Solve the following Equations2. A motorist travels for 20km at one speed, and then increased her speed by 20 kphfor next 30 km. How fast was she traveling originally if the total trip took 1 hour? APPLICATION OF QUADRATIC EQUATIONSMOTION PROBLEMS / WORK PROBLEMSMotion Problem: Distance = Rate x TimeFormula to be used in solvingWork Problem: Work = Rate x Timethese type of worded problemsExample: A car travels 10kph faster than a truck. The car goes 600 km in 5 hours less time thanit takes the truck to travel the same distance. Find the rate of each vehicle in kilometers perhour.dStep 1. Representation of the unknownCar600x+ 10600Let x = rate of the truckx+ 10x + 10 = rate of the carTruck600600Step 2. Working Equation: (Time spent by truck traveling 600 km) minus (time spent by cartraveling 600 km) is 5600600= 5x+10Step 3. Solve for x[600600x(x + 10)5 (x+10)(x) clear the equationx+10- combine similar term- reduce the equation by dividing each term by 5- Factor the quadratic expression- equate each factor to zero.600x + 6000 – 600x = 5x2 + 50x5x? + 50x – 6000 = 0x2 + 10x - 1200 = 0(x + 40)(x – 30) = 0x + 40 = 0,x –- 30 = 0- solve for xx = -40, x = 30Note: -40 can not be rate of the car because when it comes to the rate should be positive, sothe rate of the car is 30 kph.Answer: Therefore, the rate of the car is 30 kph and the rate of the truck is 40Okph.

Accepted Answer

Answered: Image /qna-images/answer/b707e355-c004-45e1-934d-54bdccb520b4.jpg

2. A motorist travels for 20km at one speed, and then increased her speed by 20 kph for next 30 km. How fast was she traveling originally if the total trip took 1 hour?