Respuesta :
Answer:
Speed of faster train equals 29 mph
Explanation:
Let the speed of slower train be 'x' miles per hour and the speed of faster train be 'y' miles per hour.
Distance that slower train covers in 2 hours=[tex]2\times x miles[/tex]
Distance that faster train covers in 2 hours=[tex]2\times y miles[/tex]
Since they move at right angles the distance between them can be found by Pythagoras formula as
[tex]d^{2}=(2x)^{2}+(2y)^{2}\\\\d^{2}=4(x^{2}+y^{2})\\(70.46)^{2}=4(x^{2}+y^{2})\\\\\therefore (x^{2}+y^{2})=\frac{(70.46)^{2}}{4}\\\\(x^{2}+y^{2})=\frac{4964.6}{4}\\\\(x^{2}+y^{2})=1241.15[/tex]
It is given that [tex]y=x+9[/tex]
Using this in the above equation we get
[tex](x^{2}+y^{2})=1241.15\\\\x^{2}+(x+8)^{2}=1241.15\\2x^{2}+16x+64=1241.15\\2x^{2}+16x-1177.15=0[/tex]
This is a quadratic equation in 'x'
Comparing with standard quadratic equation [tex]ax^{2}+bx+c[/tex] we get value of x as
[tex](x^{2}+y^{2})=1241.15\\\\x^{2}+(x+8)^{2}=1241.15\\2x^{2}+16x+64=1241.15\\2x^{2}+16x-1177.15=0\\\\x=\frac{-16\pm \sqrt{(16)^{2}-4\times 2\times -1177.15}}{2\times 2}\\\\x=\frac{-16\pm 98.35}{4}\\\\x=20.58mph(\because speed\neq <0)[/tex]
Thus speed of faster train = 28.58 mph
Speed of faster train = 19 mph
Answer:
The faster train travels at a speed of 29 miles/hr
Explanation:
Let the speed of train A be x miles/hr
So the speed of the train B is ( x - 9 ) miles/hr
After two hours, their speed will be 2x and 2( x - 9 ) respectively. and the distance between them is 70.46 miles.
So using Pythogorus theorem, we can write
[tex](2x)^{2}+(2x-18)^{2} = 70.46^{2}[/tex]
[tex]8x^{2}-72x+324 = 4964.6116[/tex]
[tex]8x^{2}-72x-4640.6116 = 0[/tex]
On solving the above equation we get
x = 29.0015 miles/hr
= 29 miles/hr
Therefore the faster train travels at a speed of 29 miles/hr
