# Pre-calc problem: Minimizing distance

• Feb 6th 2009, 12:12 PM
Juice08
Pre-calc problem: Minimizing distance
At 2:00 PM bike A is 4km north of point C and traveling south at 16km/h. At the same time, bike B is 2km east of C and traveling east at 12km/h.

a. Show that t hours after 2:00 PM the distance between the bikes is:
square root of 400t^2 - 80t + 20

b. At what time is the distance between the bikes the least?

Help would really be appreciated!
Thanks!!!
• Feb 6th 2009, 12:23 PM
skeeter
Quote:

Originally Posted by Juice08
At 2:00 PM bike A is 4km north of point C and traveling south at 16km/h. At the same time, bike B is 2km east of C and traveling east at 12km/h.

a. Show that t hours after 2:00 PM the distance between the bikes is:
square root of 400t^2 - 80t + 20

b. At what time is the distance between the bikes the least?

Help would really be appreciated!
Thanks!!!

bike A's distance from C ...

$d_A = 4 - 16t$

bike B's distance from point C ...

$d_B = 2 + 12t$

distance between the two bikes at any time t ...

$D = \sqrt{d_A^2 + d_B^2}$

how were you taught to minimize ... with or w/o calculus?
• Feb 6th 2009, 12:28 PM
Jhevon
Quote:

Originally Posted by skeeter
how were you taught to minimize ... with or w/o calculus?

the title indicates that this is for a precalculus class, so i guess w/o calculus is the way to go
• Feb 6th 2009, 12:58 PM
Juice08
Thanks!
With a calculator....i can take it from here...thank you so much guys!!!
• Feb 6th 2009, 04:24 PM
HallsofIvy
Quote:

Originally Posted by Juice08
With a calculator....i can take it from here...thank you so much guys!!!

?? How do you use a calculator to find a minimum value?
• Feb 6th 2009, 04:26 PM
skeeter
Quote:

Originally Posted by HallsofIvy
?? How do you use a calculator to find a minimum value?

graph the function and find the min ... it's really amazing what graphing calculators can do these days.