Question 1209176
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Answer: <font color=red>3.6 km</font>


Work Shown


distance = rate*time
d = r*t


Going from A to B
d = r*t
d = 4*t
t = d/4


It takes d/4 hours to travel from A to B at a speed of 4 km/hr, where d is the distance from A to B.


Similar steps will show that it takes d/6 hours to travel from B to A at a speed of 6 km/hr.
This assumes the person took the same route to go back to A, or they took a route of equal length. 


The two time values must add to 45 minutes = 45/60 = 3/4 of an hour.
Use the hour value because d/6 and d/4 are in hours.


(d/4) + (d/6) = 3/4
12*( (d/4) + (d/6) ) = 12*(3/4)
12*(d/4) + 12*(d/6) = 12*(3/4)
3d + 2d = 9
5d = 9
d = 9/5
d = 1.8 km exactly. This value hasn't been rounded.
This is the one-way distance. 
The round trip distance is double that and it is 2*1.8 = <font color=red>3.6 km</font>


Another way to solve
(d/4) + (d/6) = 3/4
(3d/12) + (2d/12) = 3/4
(3d+2d)/12 = 3/4
5d/12 = 3/4
5d*4 = 12*3
20d = 36
d = 36/20
d = (9*4)/(5*4)
d = 9/5
d = 1.8 is the one-way distance; which doubles to a round trip distance of <font color=red>3.6 km</font>


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Another approach is to convert each km per hr speed value into km per min.
To do so, divide by 60.
4 km per hr = 4/60 = 1/15 of a km per min
6 km per hr = 6/60 = 1/10 of a km per min


Using d = r*t, we get this equation when going from A to B
d = (1/15)*t
which can be rearranged to
t = 15d
This is the time it takes, in minutes, to travel from A to B.


Similar steps will show it takes 10d minutes to travel from B to A.


Total travel time = 15d+10d = 25d = 45 min
25d = 45
d = 45/25
d = (9*5)/(5*5)
d = 9/5
d = 1.8 km is the one-way distance which doubles to <font color=red>3.6 km</font> and it's the final answer.


Edit: tutor greenestamps makes a great point. I had a brainfart for some reason. My error has been fixed (changed the answer from 1.8 km to <font color=red>3.6 km</font>)
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