a boat travels 30 miles upstream in 6 hours doing downstream it can travel 78 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water
I don't know whether or not the math books still teach this, but this is what we were taught
to solve time and distance problems:
distance d
speed | time s | t
With that, being given two of the parameters, we know how to
calculate the missing parameter.
This problem gives us distance and time. We need to find speed.
Part 1: 30 mi / 6 hrs = 5 m/h
Part 2: 78 mi / 6 hrs = 13 m/h
Speed has two components, the boat's speed and the current's speed.
Going upstream, the boat's speed is decreased by the current's speed
to give the combined speed.
Going downstream, the boat's speed is increased by the current's speed
to give the combined speed.
Part 1: b - c = 5 m/h
Part 2: b + c = 13 m/h
Adding these two equations will eliminate the current's speed.
b - c = 5 m/h
+(b + c = 13 m/h)
-----------------------
2b = 18 m/h
2b = 18 m/h
b = 9 m/h
We can use either the upstream or downstream equation
to find the current's speed.
b + c = 13 m/h
9 m/h + c = 13 m/h
c = 13 m/h - 9 m/h
c = 4 m/h
We have the speed of the current is 4 miles per hour
and the speed of the boat is 9 miles per hour
