A man travels from A to B at 4 km/h and from B to A at 6 km/h. The total journey takes 45 minutes. Find the distance traveled.

Let the distance from A to B is
D

Then, the distance from B to A is also
D.

Let us use the distance formula to find
D.

We know that:

D = Speed *
Time

Given that the speed from A to B is S1 =
4

==> D = 4 * T1

Also
given that the speed from B to A is S2 = 6

==> D = 6
* T2

Then D = D

==> 4T1
= 6T2 .............(1)

But we know that the total time is
45 min

==> 45 min = 3/4
hour.

==> T1 + T2 =
3/4

We will substitute into
(1).

==> 4T1 = 6 ( 3/4 -
T1)

==> 4T1 = 9/2 -
6T1

==> 10T1 =
9/2

==> T1 = 9/20 = 0.45
hour

==> T2 = 3/4 - 9/20 = 6/20 = 0.3
hour

Then D = 4*T1 = 4* 0.45 = 1.8
km

Then, the distance is 1.8
km.