At 11am John starts along a highway at 50mph then 15 minutes later,Jimmy drives same highway at 65mph when will Jimmy catch up with John?

We know that speed = distance
/time

==> Distance = speed *
time

==> D = S*T

We
will calculate the time needed foe both John and Jimmy to travel a certain
distance.

Then the distance for both is the same and we
will assume it is D.

Now, we know that Jogns speed = 50
mph

==> S1= 50
mph

==> The time to travel D is
T1

==> D = 50 *
T1............(1)

Now we will determine the equation for
Jimmy.

The speed for Jimmy is S2 = 65
mph

The time needed to travel D is
T2

But we know that Jimmy left 15 minutes later after
John.

==> T2 = T1 - 15
minutes

15 minutes = 0.25
hour

==> T2 = T1 -
0.25

==> D = 65*(T1-
0.25)...........(2)

Now we will solve (1) and
(2).

==> 50*T1 = 65*(T1 -
0.25)

==> 50T1 = 65T1 -
16.25

==> 15*T1 =
16.25

==> T1 = 16.25 / 15
=13/12

13/12 hours = 1 1/12 hours = 1 hour and 5
minutes

Then Jimmy will catch up with John after one hour
and 12 minutes since John left.

John left at
11.

Then 11 + 1:05 =
12:05pm

Then Jimmy will catch up with John at
12:05 pm.