Math question need help

Question

A motorboat travels 165 Kilometers in 5 hours going upstream. It travels 305 kilometers going down stream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current ?

Answer 1

First, let's figure out the speed of the boat.

Speed is distance divided by time, so the speed upstream (against the current) is 165/5 = 33Kph

The speed downstream is 305 / 5 = 61 Kph

The difference is 61-33 = 28 Kph. The speed of the current will be exactly half of that. Going with the current will speed the boat up by 14 kph, and going against the current will slow the boat down by 14 kph, giving us a total difference in speed of 28 kph.

The speed of the boat in still water is simply the speed of the boat with the current, minus the speed of the current. 61 - 14 = 47kph

We could also find it by taking the speed of the boat against the current and adding the speed of the current (33 + 14 = 47) or by finding the average of the boat speeds with and against the current (33+61)/2 = 47