Let the Distance between A and B be : C km
Given : The Man Travels from A to B at a Speed 4 km/h
⇒ The Man Travels 4 km in One Hour during his Journey from A to B
⇒ [tex]The\;Man\;Travels\;One\;km\;in\;\frac{1}{4}\;Hour\;during\;his\;Journey\;from\;A\;to\;B[/tex]
⇒ [tex]The\;Man\;Travels\;C\;km\;in\;\frac{C}{4}\;Hour\;during\;his\;Journey\;from\;A\;to\;B[/tex]
Given : The Man Travels from B to A at a Speed 6 km/h
⇒ The Man Travels 6 km in One Hour during his Journey from B to A
⇒ [tex]The\;Man\;Travels\;One\;km\;in\;\frac{1}{6}\;Hour\;during\;his\;Journey\;from\;B\;to\;A[/tex]
⇒ [tex]The\;Man\;Travels\;C\;km\;in\;\frac{C}{6}\;Hour\;during\;his\;Journey\;from\;B\;to\;A[/tex]
⇒ [tex]The\;Total\;Time\;Taken\;by\;the\;Man = \frac{C}{4} + \frac{C}{6} = \frac{3C + 2C}{12} = \frac{5C}{12}\;Hour[/tex]
We know that One Hour contains 60 Minutes
⇒ The Total Time taken by Man = [tex]\frac{5C}{12}\times60\;Min = 25C\;Min[/tex]
Given Total Time Taken by Man is 45 Minutes
⇒ 25C = 45
⇒ [tex]C = \frac{45}{25} = 1.8\;km[/tex]
But the Total Distance Traveled by the Man is 2C
⇒ 2C = 2 × 1.8 = 3.6 km
⇒ The Total Distance Traveled by the Man is 3.6 km
