On a float​ trip, Kim traveled 30 miles downstream in the same amount of time that it would take her to row 18 miles upstream. If her speed in still water is 8 ​mph, find the speed of the current.

Answer 1

Let x= speed of the current

rate downstream = 8+x (you go faster with the current)

rate upstream = 8-x (you go slower against the current)

distance downstream = 30

distance upstream = 18

Formulas:

Distance = Rate x Time

Therefore, Time = Distance/Rate

Time downstream = Time upstream for this problem

Distance downstream/Rate downstream = Distance upstream/Rate upstream

Plugging everything in

30/(8+x)=18/(8-x) Solve - first step cross multiply

30(8-x)=18(8+x) Distribute to clear parenthesis

240-30x=144+18x Add 30 x to both sides

240-30x+30x=144+18x+30x Simplify

240=144+48x Subtract 144 from both sides

240-144=144+48x-144 Simplify

96=48x Divide both sides by 48

96/48=48x/48

x=2

The speed of the current is 2 mph