Distance = Rate x Time
Let x = rate of the current
6 times the speed of the current = 6x
The rate upriver ( going against the current) would be 6x -x = 5x
The rate downriver ( going with the current ) = 6x+x = 7x
Time to travel up river = 150 miles / 5x
Time to travel down river = 350 / 7x
It took 3 hours more to go down river
We now have 150/5X +3 = 350/7x
Simplify 150/5x by dividing 150 by 5 to get 30/x
Simplify 350/7x by dividing 350 by 7 to get 50/x
We now have 30/x +3 = 50/x
Remove fractions by multiplying every term by x
30 + 3x = 50
Subtract 30 from each side:
3x = 20
Divide both sides by 3 to get x
x = 20/3
x = 6.67 ( speed of the current)
The rate of the boat in still water from above is 6x
6x = 6 *6.67 = 40 miles per hour