Optimization problem: Build road joining school and expressway that enables...

[optimizationh8tr]

The question is " you are asked to build a road joining the school and the expressway that enables the shortest possible time to reach home
a) how should this be done if the speed limit is 60 km/h on the road and 100km/h on the expressway Note: The perpendicular distance from the school to the expressway is 15km and your house is 25 km down the expressway

b) based on your route what time should you home to get to school on time (assuming there is no traffic and every light is green)

can someone show me how to start this and help me through the rest becasue i dont know where to start

 

[Deleted member 4993]

The question is " you are asked to build a road joining the school and the expressway that enables the shortest possible time to reach home
a) how should this be done if the speed limit is 60 km/h on the road and 100km/h on the expressway Note: The perpendicular distance from the school to the expressway is 15km and your house is 25 km down the expressway

b) based on your route what time should you home to get to school on time (assuming there is no traffic and every light is green)

can someone show me how to start this and help me through the rest becasue i dont know where to start

Look at a similar problem at:

http://archives.math.utk.edu/visual.calculus/3/applications.3/

 

[stapel]

The question is:

You are asked to build a road joining the school and the expressway that enables the shortest possible time to reach home.

a) How should this be done if the speed limit is 60 km/h on the road and 100km/h on the expressway? Note: The perpendicular distance from the school to the expressway is 15km, and your house is 25 km down the expressway.

b) Based on your route, what time should you [leave] home to get to school on time (assuming there is no traffic and every light is green)?

I have made some corrections to the exercise's punctuation, etc. Does the statement make a little more sense now? (You may want to point out, in class, the errors, as you may not be the only student confused by the sloppy writing.) (I'm assuming that you exercised your "due diligence" in copying the original exercise completely and exactly.)

can someone show me how to start this and help me through the rest becasue i dont know where to start

Start with the algebra:

Draw a picture, with an horizontal line for the expressway and a vertical line for the current straight-line distance of the school from that expressway. You labelled the horizontal length as "25" and the vertical length as "15". You drew a slanty line, starting from somewhere along the horizontal expressway (between your house and the vertical line) and ending at the school. You labelled the slanty line with some variable (let's call it "r", for the length of the "road"), and noted that you had a right triangle. You plugged in the velocity information to create expressions for the time on each leg of the journey, using the "d = rt" formula you learned back in algebra. You added the times for the two legs, set this equal to a functional name (let's call it "f(r)"), and minimized. And... then what?

Please be complete. Thank you!

 

[optimizationh8tr]

so would it be
d=rt
15=60T
T=60/15
T=4

25=100T
T=100/25
T=4
4+4=8
am i somewhat one the right path

 

[stapel]

so would it be
d=rt
15=60T
T=60/15
T=4

Where does this (algebraically) take into account the differing entry-points of the road on the expressway? Where are you taking (calculus) derivatives to minimize travel time?

Are you in a calculus class, or are you trying to figure out how to "study" for a placement test? Because your "work done" seems to show that you may not be familiar with pre-calculus algebra....