Question

Solving a distance, rate, time problem using a system of linear

A motorboat travels 124 kilometers in 4 hours going upstream. It travels 180 kilometers going downstream 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

• boat: 38 km/h
• current: 7 km/h

Explanation:

Let b and c represent the rates of the boat and current, respectively. The speed upstream is ...

speed = distance/time

b -c = (124 km)/(4 h) = 31 km/h

And the speed downstream is ...

b +c = (180 km)/(4 h) = 45 km/h

Adding the two equations gives ...

2b = 76

b = 38

From the first equation, ...

c = b -31 = 38 -31 = 7

The rate of the boat in still water is 38 km/h; the rate of the current is 7 km/h.