On Sunday John left the place A for B at 3:30 am and on the same day

Solution:

Let the rate of John be x and the rate of Carsten be y. When they met at 12:30pm, John had been traveling for 9 hours and Carsten had been traveling for 4 hours; thus they covered distances of 9x and 4y, respectively. After meeting, John has a distance of 4y to travel, which he will complete in 4y/x hours. Similarly, Carsten has a distance of 9x to travel and he will cover this distance in 9x/y hours. We are told that it took equal time for the two to reach their destinations; thus:

4y/x = 9x/y

4y^2 = 9x^2

2y = 3x or 2y = -3x

Since x and y are rates, neither can be negative; thus we can discard the possibility of having 2y = -3x.

Recall that it takes John 4y/x hours to complete his journey. Rewriting 4y/x = 12y/3x and substituting 2y = 3x, we see that it took John 12y/2y = 6 hours to reach his destination. Since they met at 12:30pm, John will reach his destination at 12:30pm + 6 hours = 6:30pm.

Notice that we will obtain the same result if we use Carston’s time of 9x/y (in which case we would rewrite 9x/y as 18x/2y and replace 2y by 3x).

Answer: B