time distance rate question

Question

micaela left the hardware store and traveled toward her friend house at an average speed of 25 kmh nicole left some time later traveling in same direction at average speed of 30 kmh after travelling for five hours nicole caught up with micaela how long did micaelal travel before nicole caught up

 

micaela time is t

 

             d   =   t   *  r 

micaela           25 *  t+5

nicole          = 30  *  5          

 

my confusion is nicole left some time later so our time should be nicole time is 5 and micaela time should be t+5 because micaela stars travel earlier than nicole but get wrong answer

 

please explain me full fundamental concept 

Answer 1

distance=rate*time

d=r*t

d=25t

d=30*5

d=150

25t=150

t=150/25

t=6 hours

Answer 2

Fundamentally, think of three points in time:

Micaela leaves: time = 0 (hours)

Nicole leaves: time = t (hours) [Micaela has travelled for t hours at this point]

Nicole reaches Micaela = t + 5 (hours)

 

Thus, we know that Micaela has been travelling for t + 5 hours.

 

From here, we know that the total distance Micaela has travelled is:

25*(t + 5) = 25t + 125 (km)

 

Now, we know that Nicole has travelled for 5 hours at 30 kmh so Nicole has travelled:

30*(5) = 150 km

 

Since they are at the same point at this time, we can equate these distances:

150 = 25t + 125

 

From here it's algebra:

25 = 25t

t = 1 hour.

 

Thus, Micaela has travelled for 1 + 5 = 6 hours.