Question

Bob can row 13mph in still water. The total time to travel downstream and return upstream to the starting point is 2.6 hours. If the total distance downstream and back is 32 miles. Determine the speed of the river (current speed)

Answer 1

"s" is the river speed 16 miles is the one-way distance

Time = distance / velocity

2.6 = [16 / (13 + s) ] + [16 / (13 -s) ]

That solves to s = 3 miles per hour

Explanation:

Answer 2

Answer: the speed of the current is 3 mph

Explanation:

Let x represent the speed of the river current.

Bob can row 13mph in still water. Assuming that while rowing upstream, he rowed against the current, this means that his total speed upstream is (13 - x) mph

Assuming that while rowing downstream, he rowed with the current, this means that his total speed downstream is (13 + x) mph.x

If the total distance downstream and back is 32 miles. Assuming the distance upstream and downstream is the same, then the distance upstream is 32/2 = 16 miles. Distance downstream is also 16 miles.

Time = Distance/speed

Time taken to row upstream is

16/(13 - x)

Time taken to row downstream is

16/(13 + x)

If total time spent is 2.6 hours, it means that

16/(13 - x) + 16/(13 + x) = 2.6

Cross multiplying, it becomes

16(13 + x) + 16(13 - x) = 2.6(13 + x)(13 - x)

= 208 + 16x + 208 - 16x = 2.6(169 - 13x + 13x - x²)

416 = 2.6(169 - x²)

416/2.6 = 169 - x²

160 = 169 - x²

x² = 169 - 160 = 9

x =√9

x = 3