Respuesta :
Answer:
they will meet 270 km far away from Frankfurt
Step-by-step explanation:
Given :The distance between Frankfurt and Prague is 432.5 km. Alex left Frankfurt at 10 AM and started traveling to Prague at 60 km/h. At noon Michael started traveling on the same route from Prague to Frankfurt at 65 km/h.
To Find: . How far away from Frankfurt will they meet?
Solution:
Speed of Alex is 60 km/h.
Speed of Michael is 65 km/h.
Let x be the distance traveled by Alex from Frankfurt till he met Michael
Let y be the distance traveled by Michael from Prague till he met Alex
Since total distance between Frankfurt and Prague is 432.5 km
So, x+y = 432.5 --a
Let t+2 be the time for which Alex traveled and meet Frankfurt
Since Michael start travelling after two hours
So, time taken by him is t+2-2 = t hours
So, Time of Alex for distance x = distance /speed = x/60
So, [tex]t+2 =\frac{x}{60}[/tex]--b
now time for Michael = distance /speed= y/65
So, [tex]t=\frac{x}{65}[/tex] --c
Now to eliminate t
subtract c from b
⇒[tex]\frac{x}{60} -\frac{y}{65} =2[/tex]
⇒[tex]\frac{13x-12y}{780} =2[/tex]
⇒[tex]13x-12y =1560[/tex] ---d
Now solving a and d
Substitute value of x from a in d
⇒[tex]5622.5-13y-12y =1560[/tex]
⇒[tex]5622.5-25y =1560[/tex]
⇒[tex]5622.5-1560 =25y[/tex]
⇒[tex]4062.5 =25y[/tex]
⇒[tex]\frac{4062.5}{25} =y[/tex]
⇒[tex]162.5 =y[/tex]
So, to find x use equation a
x+162.5 = 432.5
x= 432.5-162.5
x=270 km
Thus they will meet 270 km far away from Frankfurt
