Sam's wheel?

Question

Sam's wheel?
Sam's four wheel drive is capable of speeds of 40km/h across country and 80km/h along roads.he receives a call asking him to get home as quickly as possible.At the time of the call he was 15km from a point P which lies on a straight road and a distance of 35km from home,furthe along the road.

Sam decides to drive across country directly to some point between home and the point P on the road.

a) If the distance that Sam travels on the road is x how far does he travel across country?

b) using t=d/v obtain an expression for the total amount of time Sam spends on his journey.

c) How far does Sam need to travel on the road for his quickest route home?
What is the minimum possible time Sam can spend travelling (to the nearest minute)?

Answer 1

Since the road is 35 miles long, the distance he does NOT travel on the road is 35-x. This, with 15 km, forms a right triangle whose hypotenuse is the distance he travels cross country. If that distance is q, then q^2 = 225 + (35-x)^2

His total time is the sum of times on each leg of the journey"
Road time = x/80
CC time = q/40, q defined above.
Total time = x/80 + q/40

To determine the shortest time, we take d(total time)/dt, and set it equal to zero.
I'm turning in right now, so you can do that for me.

Answer 2

I dint follow the description but the path requiring shortest time can be found by assuming it to be the path of light.so use snells law taking the two surfaces as two different media with velocity of light in one twice that in the other.