Problem: rower rows 6 mi. up & 4 mi down in 80 min, current speed 3 mph, whats the speed of rower?
algebraic word problem
The rower's speed will be designated s. Going upstream, the speed is s - 3. Going downstream,
the speed is s + 3.
The time to row upstream is t1. The time to row downstream is t2.
t1 = 6/(s - 3)
t2 = 4/(s + 3)
t1 + t2 = 4/3 hr
6/(s - 3) + 4/(s + 3) = 4/3
3(6/(s - 3) + 4/(s + 3)) = 3 * 4/3
18/(s - 3) + 12/(s + 3) = 4
(s - 3)(s + 3)(18/(s - 3) + 12/(s + 3)) = 4(s - 3)(s + 3)
18(s + 3) + 12(s - 3) = 4(s - 3)(s + 3)
18s + 54 + 12s - 36 = 4(s^2 - 3s + 3s - 9
30s + 18 = 4s^2 - 36
4s^2 - 30s - 54 = 0 Factor this.
(2s - 18)(2s + 3) = 0
Set each factor to zero and solve for s.
(2s - 18) = 0
2s = 18
s = 9
(2s + 3) = 0
2s = -3
s = -1.5
A negative speed implies that the rower is rowing
in the wrong direction, so disregard that.
The rower's speed must be 9 mph. Check it.
t1 = 6/(9 - 3)
t1 = 6/6
t1 = 1 hr
t2 = 4/(9 + 3)
t2 = 4/12
t2 = 1/3 hr
1 hr + 1/3 hr = 4/3 hr
1 1/3 hr = 4/3 hr
It checks, so the rower's speed is 9 mph.
