SOLUTION: If you are planning to make a 24 mile round trip while canoeing in a river with a current of 2 mph, how fast will you have to paddle to make the trip in 4.5 hours?
Algebra ->
Rate-of-work-word-problems
-> SOLUTION: If you are planning to make a 24 mile round trip while canoeing in a river with a current of 2 mph, how fast will you have to paddle to make the trip in 4.5 hours?
Log On
Question 353742: If you are planning to make a 24 mile round trip while canoeing in a river with a current of 2 mph, how fast will you have to paddle to make the trip in 4.5 hours? Found 3 solutions by mananth, robertb, josmiceli:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Let him paddle at x mph.
With current the speed will be x+2 mph
against current the speed will be x-2 mph.
Time forward + time return = 4.5 hours = 9/2 hours
12/(x+2)+12/(x-2)=9/2
..
12(x-2)+12(x+2) /(x+2)(x-2)= 9/2
12x-24+12x+24 / (x+2)(x-2)=9/2
24x/(x+2)(x-2)= 9/2
2*24x=9(x+2)(x-2)
48x=9*(x^2-4)
48x=9x^2-36
9x^2-48x-36=0
/3
3x^2-16x-12 =0
3x^2-18x+2x-12=0
3x(x-6)+2(x-6)=0
(3x+2)(x-6)=0
x=6 mph. Ignore the negative value
He will have to paddle at 6 mph.
m.ananth@hotmail.ca
You can put this solution on YOUR website! distance up the river = 12 miles
let x = speed of canoe. Rate of canoe with respect to the river = x-2
distance down the river = 12 miles.
rate of canoe with respect to the river = x+2.
From the formula . Thus .
The equation is the same as after simplification. . . .
Thus miles per hr.
You can put this solution on YOUR website! Let = paddle speed
Let = time to go upstream
Let = time to go downstream
given: hrs
Distance upstream: mi
Distance downstream: mi
Speed of current: mi/hr
------------------------------
Going upstream:
(1)
Going downstream:
(2)
From (1) and (2):
(1)
(2)
Add (1) and (2):
Multiply both sides by
Use quadratic formula
You must paddle 6 mi/hr
check answer:
(1)
(1) hrs
and
(2)
(2)
OK
