# Thread: preparation for optimizatio word problem

1. ## preparation for optimizatio word problem

This is in preparing us for optimization in calculus, yet i dont understand how this diagram will look or how to solve it, can someone give someone pointers?

A man can row at 24 km/h, and run at 7 km/h. He needs to get from a point A, on the south bank of a stretch of still water, to point B on the north bank of the water. The direct distance from A to B is 25 km, and the water is 24 km wide. He starts rowing with an angle theta between North and the direction in which he rows. Find an expression for the time T he will take to get from A to B, in terms of theta.

What is the speed of running use for?

2. A man can row at 24 km/h, and run at 7 km/h.
sure this isn't backwards?

The direct distance from A to B is 25 km
and this ... sure it's not distance from A to B down (parallel) to the beach?

3. its not backwards, and i believe the direct distance is the hypotenuse of right triangle.

thanks

4. I believe the theta represents the angle between the north and the direction he is rowing.

5. These type of "time" optimization starter problems are usually designed so that part rowing and part running will achieve the least amount of time. There are some (like this) that yields the least time for all rowing (or all running) depending on the problem set-up ... but these usually don't come until after you've solved a couple of starter problems.

No matter ...

$t$ = time in hrs

$x$ = distance shown in the sketch

$t = \dfrac{\sqrt{24^2 + x^2}}{24} + \dfrac{7-x}{7}$

obviously, the minimum time will be a bit over an hour if the person rows directly from A to B. you can check the minimum w/ a graph on your calculator

This is what happens when a problem's parameters aren't checked against the real world ... no thought at all in setting it up, imho.

it would take an Olympic athlete to row a boat at a rate of 24 km/hr for over an hour.

my grandmother can walk faster than 7 km/hr.

6. Thank you for the very clear picture. I can now imagine what is happening. Just wondering, what would be the difference in terms of solving it in theta t(theta) compared to your answer?

7. Originally Posted by ASUSpro
Thank you for the very clear picture. I can now imagine what is happening. Just wondering, what would be the difference in terms of solving it in theta t(theta) compared to your answer?
put $\theta$ in the diagram and solve for $x$ in terms of $\theta$ ... then sub in for $x$ in the equation.

8. very strange. even after solve for x in term of theta and plugging it in.. still wasn't able to achieve the correct answer. Or is it my algebra in simplifying that's off?

9. Originally Posted by ASUSpro
very strange. even after solve for x in term of theta and plugging it in.. still wasn't able to achieve the correct answer. Or is it my algebra in simplifying that's off?
what "correct answer" did you not achieve? ... and, what answer did you arrive at?