Answer:
(a)In the attachment
(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.
Step-by-step explanation:
(a)In the attachment
(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)
First, let us determine length of line RM.
Using Pythagoras theorem

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.
Time Taken = Distance/Time
Time taken on the road 
Time taken on the highway 
Total time taken to travel, T 
Minimum time taken occurs when the derivative of T equals 0.

Square both sides

The road should be built such that it joins the highway at 19.52km from the point P.
In fact,

The formula to find the Length of the arc = (2r) (θ / 360°)
Substituting the values
Length of the arc = (2) (40) (324° / 360°)
By further calculation
= (80) (0.9)
So we get
= (80) (3.14) (0.9)
= 226.08 cm.
Therefore, the length of the arc is 226.08 cm.
Hope this helps
Answer: this is a INVERSE choice C
50*25= 1250
2mins 15seconds= 135 seconds
135*3= 405
1250-405 = 845
Your score is 845