SOLUTION: Here is another headache for me! A motorboat maintained a constant speed of 20 miles per hr relative to the water in going 24 miles upstream and the returning. The total time fo

Algebra ->  Formulas -> SOLUTION: Here is another headache for me! A motorboat maintained a constant speed of 20 miles per hr relative to the water in going 24 miles upstream and the returning. The total time fo      Log On


   

Question 852414: Here is another headache for me!
A motorboat maintained a constant speed of 20 miles per hr relative to the water in going 24 miles upstream and the returning. The total time for the trip is 2.5 hours.
Use this information to find the speed of the current.
Please help. I really need an answer.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This part of your description is bad: "a constant speed of 20 miles per hr relative to the water".

The trip distance is also not perfectly clear; I'm assuming as 24 miles in either direction.
Try to put data into a table.

__________________speed________time_______distance
Upstream__________20-c_________(___)______24
Downstream________20+c_________(___)______24
TOTAL__________________________2.5

Uniform rate for travel follows RT=D, so fill the time information as T=D%2FR.

__________________speed________time_______distance
Upstream__________20-c_________24%2F%2820-c%29______24
Downstream________20+c_________24%2F%2820%2Bc%29______24
TOTAL__________________________2.5

The time sum equation has only the variable, c as unknown. That is the speed of the current of the river.
highlight_green%2824%2F%2820-c%29%2B24%2F%2820%2Bc%29=2.5%29.

SOLVING THE EQUATION
LCD is (20-c)(20+c).
24%2820%2Bc%29%2B24%2820-c%29=2.5%2820%5E2-c%5E2%29
24%2820%2Bc%2B20-c%29=%285%2F2%29%28400-c%5E2%29
24%2A20%2A2=5%28400-c%5E2%29
720=2000-500c%5E2
720-2000=-500c%5E2
500c%5E2=2000-720
500c%5E2=1280
50c%5E2=128
c%5E2=128%2F50=2.56
highlight%28c=1.6%29