Question 593007
1. Mike can row in still water at a speed twice that of the current in a certain river.
 It takes Mike 2 hours more to row 10 km up the river than it takes him to row 15 km down the river.
 What is the speed of current in the river?
:
Let r = speed of current of the river
It states, "row in still water at a speed twice that of the current", therefore
2r = his rowing speed in still water
Then
2r - r = r, effective speed upstream
2r + r = 3r, effective speed downstream
:
Write time equation
Upriver time - downriver time = 2 hrs
{{{10/r}}} - {{{15/(3r)}}} = 2
multiply by 3r
3r*{{{10/r}}} - 3r*{{{15/(3r)}}} = 3r(2)
Cancel the denominators
3(10) - 15 = 6r
30 - 15 = 6r
15/6 = r
r = 2.5 km/hr is the speed of the current
:
:
Check that out, rowing speed in still water will be 5 km/hr, find the times
10/2.5 = 4hrs
15/7.5 = 2hrs
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difference: 2 hrs