Can someone babywalk me through this? My calculations are no where near the answer I was given.

Two homes are located 4 miles apart, each 1 mile from a road that parallels the ocean.
I can jog 4 mph along the road, but only 3mph in the sand.
Because of a river between the two houses, it is necessary to jog on the sand to the road, continue on the road, and then jog on the sand to get from one house to the other.
For 0° < Θ < 90° , the time to get from one house to the other is a function of Θ, as shown.

http://pasteboard.co/NumJMHV.jpg

T(30°)=1.47 (rounded to nearest hundreth after finding the final anwer) in hours.
My question is how? I'm just looking for an explanation so that I may be able to solve similar questions. Thanks.

This post was edited by Iffy00 on Feb 1 2015 11:37am

are you asking how to derive the equation? or are you saying you put T(30d) and got a different answer? considering you didn't give a question, i'm not sure what you're asking

This post was edited by carteblanche on Feb 1 2015 12:00pm

Your path is symmetrical in regards to the river.
On the right part :
2 - x miles to travel along the road, at a speed of 4 mph,
y miles to travel through the sand, at a speed of 3 mph.

Express x and y in terms of θ :
x = 1 / tan θ
y = 1 / sin θ

Total time for your travel ( for each part, time = distance / speed ) :

T(θ) = 2 * ( ( 2 - 1 / tan θ )/4 + ( 1 / sin θ ) / 3 )

T(θ) = 1 - 1 / 2.tan θ + 2 / 3.sin θ

This post was edited by feanur on Feb 1 2015 12:04pm

check the picture for the equation.

This is the equation so far, but I'm still have trouble understanding.

T(30°) = 1+2/3(1/2)-1/2(√3/3) = 1.47 (how?)
Babysteps please

sin 30° = 0.5
tan 30° = 1 / sqrt(3)

1 / sin 30° = 2
1 / tan 30° = sqrt(3)

T(30°) = 1 - sqrt(3)/2 + (2/3)x2
T(30°) = 7/3 - sqrt(3)/2

take an approximate value of sqrt(3) :
T(30°) ~ 1.467 hour

ya... I was thinking of this for a while, I still don't 100% understand but at least I know that I can now calculate it correctly.

Thanks for the help