two trains are 330 miles apart, and their speeds differ by 20mph. Find the speed of each train if they are traveling towards each other and will meet in 3 hours.
a million. Width = x length = 2x - 12 Diagonal = 30 as rapidly as you draw the rectangle and label its factors, you would be unsleeping which you're easily coping with a pythagorean trangle with legs x and 2x - 12, and a hypotenus of 30. so as that's comparable to: a = x b = 2x - 12 c = 30 given which you already know that c^2 = a^2 + b^2 (Pythagorean Theorem), you may desire to swap the values: 30^2 = x^2 + (2x-12)^2 from suitable acceptable right here, you fairly therapy for x... 900 = x^2 + (4x^2 - 48x + a hundred 40 4) [squaring the binomial] 900 = 5x^2 - 48x + a hundred 40 4 [simplifying] 0 = 5x^2 - 48x + a hundred 40 4 - 900 [consisting of 900 to the two factors] 0 = 5x^2 - 48x - 756 we've a quadratic equation. you may desire to the two factor that or use the quadratic formulation. I many circumstances elect factoring yet utilising the quadratic formulation is plenty much less confusing to describe. the quadratic formulation is x = (-b +/- sqrt(b^2 - 4ac)/ 2a in our equation, a = 5, b = -40 8 and c = -756 so, plugging indoors the values, we've x = (40 8 +/- sqrt(40 8^2 - 4(5)(-756))/2(5) x = (40 8 +/- sqrt(17424)) /10 x = (40 8 +/- 132)/10 case1: x = (40 8 + 132)/10 x = a hundred 80/10 x = 18 case2: x = (40 8 - 132)/10 x = -80 4/10 x = -8.4 we've 2 values of x, this is 18 and -8.4 you may desire to now now no longer have a unfavourable width, suitable? so the correct fee is extremely 18. W = x L = 2x - 12 so W = 18 L = 24 psi do now no longer know the way specific you like it so there. I easily have not have been given adequate time to therapy all of them and make clean suitable acceptable right here in guidance so i bypass to easily bypass away that to the persons suitable acceptable right here. additionally, i do advise which you do plenty and much and dissimilar practice. heavily, that helps :D
Answers & Comments
Verified answer
Speed of the slower train—x:
3(x + x + 20) = 330
2x + 20 = 110
x + 10 = 55
x = 45
Speed of the faster train:
= 45 + 20
= 65
Answer: 45 mph and 65 mph are the speeds of the trains.
Proof (they meet in 3 hours):
= 330 mi/(45 mph + 65 mph)
= 330 mi/110 mph
= 3 hours
a million. Width = x length = 2x - 12 Diagonal = 30 as rapidly as you draw the rectangle and label its factors, you would be unsleeping which you're easily coping with a pythagorean trangle with legs x and 2x - 12, and a hypotenus of 30. so as that's comparable to: a = x b = 2x - 12 c = 30 given which you already know that c^2 = a^2 + b^2 (Pythagorean Theorem), you may desire to swap the values: 30^2 = x^2 + (2x-12)^2 from suitable acceptable right here, you fairly therapy for x... 900 = x^2 + (4x^2 - 48x + a hundred 40 4) [squaring the binomial] 900 = 5x^2 - 48x + a hundred 40 4 [simplifying] 0 = 5x^2 - 48x + a hundred 40 4 - 900 [consisting of 900 to the two factors] 0 = 5x^2 - 48x - 756 we've a quadratic equation. you may desire to the two factor that or use the quadratic formulation. I many circumstances elect factoring yet utilising the quadratic formulation is plenty much less confusing to describe. the quadratic formulation is x = (-b +/- sqrt(b^2 - 4ac)/ 2a in our equation, a = 5, b = -40 8 and c = -756 so, plugging indoors the values, we've x = (40 8 +/- sqrt(40 8^2 - 4(5)(-756))/2(5) x = (40 8 +/- sqrt(17424)) /10 x = (40 8 +/- 132)/10 case1: x = (40 8 + 132)/10 x = a hundred 80/10 x = 18 case2: x = (40 8 - 132)/10 x = -80 4/10 x = -8.4 we've 2 values of x, this is 18 and -8.4 you may desire to now now no longer have a unfavourable width, suitable? so the correct fee is extremely 18. W = x L = 2x - 12 so W = 18 L = 24 psi do now no longer know the way specific you like it so there. I easily have not have been given adequate time to therapy all of them and make clean suitable acceptable right here in guidance so i bypass to easily bypass away that to the persons suitable acceptable right here. additionally, i do advise which you do plenty and much and dissimilar practice. heavily, that helps :D