Answer :
The required distance is 16.40 km.
This problem can be solved if we know the concept of speed, time and distance.
We know the speed=[tex]\frac{distance}{time}[/tex]
To solve the problem let us assume that the total distance between the workplace and home is x km.
Given that his speed while going from home to work is 45 mph and while returning is 35 mph.
Time for the complete journey is [tex]\frac{5}{6}hr[/tex].
Now according to question;
[tex]\frac{x}{45}+\frac{x}{35}=\frac{5}{6}[/tex]
⇒[tex]\frac{7x+9x}{315}=\frac{5}{6}[/tex]
⇒[tex]16x=\frac{5*315}{6}[/tex]
⇒ [tex]x=\frac{5*315}{6*16}[/tex]
∴ [tex]x=16.40\ km[/tex]
So, the required distance is 16.40 km.
To learn more about speed, distance and time visit the link:
https://brainly.com/question/15256256
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