(10pts) 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. how far away from frankfurt will they meet?

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,  --b

now time for Michael = distance /speed= y/65

So,   --c

Now to eliminate t

subtract c from b

⇒

⇒

⇒ ---d

Now solving a and d

Substitute value of x from a in d

⇒

⇒

⇒

⇒

⇒

⇒

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