Power Travel
May 12th, 2007
MATH 11 WORD PROBLEMS SOLVE BY ELIMINATION HELP?
A boat at constant power travels 60 km upriver in 3h and returns in 2h, what is the speed of the boat a) relative to the water b) current?
THE ANSWER IS (25, 5)
To solve this, think of the speed of the boat as the variable x. The current is another constant variable, we'll call it y, that will increase or decrease the speed of the boat. Add it to x if you are going with the stream as it speeds up the boat, or subtract it from x if you go going upstream because it is now a burden. It does not work like this in real life, but since math is arbitrary, we'll just go with this way for now.
3x-3y = 60
2x+2y = 60
The first equation denotes that the boat takes longer (3h) to reach 60km upstream because it is slowed by the current. The second is the exact opposite (2h). Now use elimination to solve for either variable:
2(3x)-2(3y) = 2(60)
- 3(2x)+3(2y) = 3(60)
__________________
0x - 12 y = -60
-12y = -60
y = 5
The current is 5km/h. Substitute it into either equation and solve for x.
3x-3(5) = 60
3x - 15 = 60
3x = 75
x = 25
The speed at which the boat travels relative to the water (without current aiding or obstructing it) is 25km/h.
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