Question

A motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.

please help slove and steps

Answer 1

Going upstream: 432 km / 6 hours = 72 km/h
Going downstream: 384 km / 4 hours = 96 km/h
Going upstream against the current means that the effective speed is:
r_boat - r_current = 72
Meanwhile, going downstream with the current means;
r_boat + r_current = 96
Adding both equations (to cancel out r_current) gives:
2r_boat = 72 + 96
r_boat = 84 km/h
Substituting back into one of the original equations: r_current = 12 km/h.