College Algebra & Trigonometry, 2018a

4.9. OPTIMIZATION 253
B
x
50 km
50 − x
C
D
40 km
A
If we express the distance between B and C as x, then the distance between C and
D will be 50 − x. The distance travelled in the desert is the distance from A to C
and this is found using the Pythagorean Theorem.
AC = √ 40 2 + x 2 = √ x 2 + 1600
Since d = r ∗ t, then the time it takes travel a given distance will be d r = t.
In the case of this problem the time to travel from A to C is:
t 1 =
√
x2 + 1600
45
The time to travel from C to D is:
t 2 = 50 − x
75
So, the total travel time will be:
t = t 1 + t 2 = x2 + 1600
45
+ 50 − x
75