Sam rows up a river to camp in 3 hours. The next day he makes the return trip downstream in 1 hour. If he can row 2 mph in still water, how fast is the current?
To find out how fast the current is, we need to set up an equation using the given information.
Let's assume that the speed of the current is represented by 'c' mph.
When Sam rows up the river, his effective speed is reduced by the current's speed, so his speed relative to the ground is 2 mph - c mph. Likewise, when he rows downstream, his effective speed is increased by the current's speed, so his speed relative to the ground is 2 mph + c mph.
Given that he takes 3 hours to row upstream and 1 hour to row downstream, we can set up the following equations:
(time = distance / speed)
For the trip upstream:
3 hours = distance / (2 mph - c mph)
For the trip downstream:
1 hour = distance / (2 mph + c mph)
To find the speed of the current, we can now equate the two distances:
(distance upstream) = (distance downstream)
(distance / (2 mph - c mph)) = (distance / (2 mph + c mph))
Now, we can cross-multiply:
(distance) * (2 mph + c mph) = (distance) * (2 mph - c mph)
Simplifying the equation further:
2 mph + c mph = 2 mph - c mph
Now, isolate the variable 'c' by collecting like terms:
2c mph = -2 mph
Dividing both sides by 2 mph:
c mph = -1 mph
The negative sign indicates that the current is flowing in the opposite direction of Sam's rowing. Thus, the speed of the current is 1 mph.
Therefore, the current is flowing at a speed of 1 mph.