Question

(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?

Answer 1

they will meet 270 km far away from Frankfurt

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,
`t+2 =(x)/(60)`--b

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

So,
`t=(x)/(65)` --c

Now to eliminate t

subtract c from b

⇒
`(x)/(60) -(y)/(65) =2`

⇒
`(13x-12y)/(780) =2`

⇒
`13x-12y =1560` ---d

Now solving a and d

Substitute value of x from a in d

⇒
`5622.5-13y-12y =1560`

⇒
`5622.5-25y =1560`

⇒
`5622.5-1560 =25y`

⇒
`4062.5 =25y`

⇒
`(4062.5)/(25) =y`

⇒
`162.5 =y`

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