A man wishes to walk home, which is 10 km away down a main road and then a further 4 km down a smaller road perpendicular to the first. The man can walk at 5 km/hr along the road and can walk across the fields surrounding the area at 3 km/hr. Suppose the man was to walk along the main road for some time and then cut diagonally across the fields straight to his house (that is, without ever going on to the smaller road). The goal of this exercise is to minimize the time that the man spends walking home. To do so, first recall a relevant formula regarding time: Important Notes: . Enter the formula that is relevant to the context of this particular question. . For each box, enter one of the following words: displacement, speed, position, velocity, distance, or acceleration. . Be mindful of your spelling. For the system to mark it correctly, the spelling must be accurate. . Time = _, where a = and b = Now, determine how far the man must walk down the main road (before cutting across the field) in order to minimize his walking time. Fill in the blanks below. Important Notes: . Enter whole numbers or reduced proper/improper fractions with NO spaces between the symbols. For example, for , enter "13/8" (with NO quotation marks). . Do NOT enter decimal numbers or mixed numbers. . The minimum time that it takes for the man to get home by taking the main road and cutting across the field is hr. . The total time that it would take for the man to walk along the main road and the smaller road (without cutting across the field) is hr. . Enter T for TRUE and F for FALSE. The fastest route for the man to get home involves taking the main road followed by the smaller road (without cutting across the field)