A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?
1 Answer
The boat's speed is
Explanation:
We know that
Therefore,
#d/("speed against current") + d/("speed with current") = t_"total"#
We know that
#3 = 15/(x - 2) + 15/(x + 2)#
#3(x^2 - 4) = 15(x + 2) + 15(x - 2)#
#3x^2 - 12 = 15x + 30 + 15x - 30#
#3x^2 - 30x - 12 = 0#
#x^2 - 10x - 4 = 0#
This cannot be factored, thus we use the quadratic formula or a graphical approach. Use your graphing calculator to enter
A negative answer is impossible, so we deduce that the speed in still water of the boat is approximately
#t = 15/8.4 = 1.8 hrs#
Hopefully this helps!