A hiker starts from a camp taken as the origin on a straight trail. He executes the following sequence of walks:
• 20 m eastwards
• x m westwards
• 30 m eastwards
• y m westwards
At the end of the fourth walk he is back at the camp.
(i) Obtain a relation connecting x and y from the above data.
(ii) Given that ∣x−y∣=10m, determine the two possible ordered pairs (x,y) that satisfy both conditions.
(iii) For each ordered pair obtained in part (ii), compute the total distance covered by the hiker.
(iv) Comment on whether it is possible for two different sets of walks to have the same net displacement but different total distances.