Bill can row 3mph in still water. It takes him 3hrs36 minutes to go 3 miles upstream and return. Find the speed of the current
Let x = speed of the current.
Speed = distance/time so time = distance/speed
upstream time + downstream time = 3.6 hours
3/(3 - x) + 3(3 + x) = 3.6
3(3+x) + 3(3-x) = 3.6(3-x)(3+x)
9 + 3x + 9 - 3x = 3.6(9 - x^2)
18 = 3.6(9-x^2)
5 = 9 - x^2
x^2 = 4
x = 2
The speed of the current was 2 mph
Check:
3 - 2 or 1 mph for 3 miles upstream = 3 hours time
3 + 2 or 5 mph for 3 miles downstream = .6 hours or 36 minutes
so total time would be 3 hours 36 minutes
Jim
Comments
Let x = speed of the current.
Speed = distance/time so time = distance/speed
upstream time + downstream time = 3.6 hours
3/(3 - x) + 3(3 + x) = 3.6
3(3+x) + 3(3-x) = 3.6(3-x)(3+x)
9 + 3x + 9 - 3x = 3.6(9 - x^2)
18 = 3.6(9-x^2)
5 = 9 - x^2
x^2 = 4
x = 2
The speed of the current was 2 mph
Check:
3 - 2 or 1 mph for 3 miles upstream = 3 hours time
3 + 2 or 5 mph for 3 miles downstream = .6 hours or 36 minutes
so total time would be 3 hours 36 minutes
Jim