Suppose you are in a car (C) that that has run out of petrol 2 km away from a T-intersection (T). You know that there is a Petrol Station (G) 4 km away from the intersection – as shown in the diagram. You can walk along the road at a speed of 5 km. per hour. You could also cut across an undulating field and intersect the road closer to the petrol station (S), but your cross country walking speed will be reduced to 3 km. per hour. You must decide which option is quickest, since the petrol station closes in 1 and a half hours.
a) From the diagram, derive the following formula, which gives the total time required to walk to the garage using any straight path across the field T(x)= [square root(x^2 +4)]/3 + (4-x/5)
b) Explain the significance of the situation when x = 0, and why T(x) cannot be used to calculate the total time taken when x = 0?