Respuesta :
Distance covered = 20 km
Let x km/h be the speed pf first sky. Then, speed of second sky will be (x+2) km/h
Time = distance/speed
Therefore,
20/x - 20/(x+2) = 20 minutes = 1/3 hrs
Solving;
20(x+2) - 20(x)= x(x+2)*1/3
60(x+2) - 60(x) = x^2+2x
60x+120-60x =x^2+2x
120 = x^2+2x
x^2+2x-120 = 0
Then,
x = {-b+/- sqrt (b^2-4ac)}/2a = {-2+/- sqrt(2^2-4*a*-12)}/(2*1) = 10 or -12
Ignoring the negative value, x = 10 km/h
Therefore, the first sky is travelling at 10 km/h while the second is travelling at (10+2) 12 km/h
Let x km/h be the speed pf first sky. Then, speed of second sky will be (x+2) km/h
Time = distance/speed
Therefore,
20/x - 20/(x+2) = 20 minutes = 1/3 hrs
Solving;
20(x+2) - 20(x)= x(x+2)*1/3
60(x+2) - 60(x) = x^2+2x
60x+120-60x =x^2+2x
120 = x^2+2x
x^2+2x-120 = 0
Then,
x = {-b+/- sqrt (b^2-4ac)}/2a = {-2+/- sqrt(2^2-4*a*-12)}/(2*1) = 10 or -12
Ignoring the negative value, x = 10 km/h
Therefore, the first sky is travelling at 10 km/h while the second is travelling at (10+2) 12 km/h
The speed of both skiers will be 10 km/h. Distance is found as the product of speed and time. The given relation is used to solve the problem.
What is the distance?
Distance is a numerical representation of the distance between two objects or locations.
The distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.
The given data in the problem is;
Distance travelled = 20 km
Let the first sky's speed be y km/h. From the given conditions the second sky's speed will then be (y+2) km/h.
The distance is found as;
[tex]\rm distance = speed \times time[/tex]
[tex]\rm Time = \frac{Distance }{Speed}[/tex]
According to the question;
One skier covered the distance of 20 km 20 minutes faster than the other skier;
[tex]\rm T_1-T_2= 20 minute \\\\ \rm T_1-T_2= \frac{1}{3}\ hrs \\\\ \frac{20}{y} -\frac{20}{y+2} = \frac{1}{3}\ hrs \\\\ 20(y+2) - 20(y)= y(y+2)\frac{1}{3} \\\\ 60(y+2) - 60(y) = y^2+2y\\\\ 60y+120-60y =y^2+2y\\\\ 120 = y^2+2y\\\\ y^2+2y-120 = 0[/tex]
Furthur solving the given quadratic equation we will get;
y= 10
y=-12
(- ve) value in terms of velcity is not possible.
y= 10 km/h
Hence the speed of both skiers will be 10 km/h
To learn more about the distance refer to the link;
https://brainly.com/question/26711747
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