Nina’s toy boat travels 6 miles per hour in still water. It travels 1/4 mile upstream and back in a total time of 30 minutes. What is the speed of the current

Question

Nina’s toy boat travels 6 miles per hour in still water. It travels 1/4 mile upstream and back in a total time of 30 minutes. What is the speed of the current, rounded to the nearest tenth miles per hour?

Answer 1

Let x = speed of current

 

speed downstream = 6-x

speed upstream = 6+x

 

Distance = (Rate)(Time), so Time = (Distance)/(Rate)

 

Time upstream + Time downstream = 0.5 hours

 

(1/4)/(6+x) + (1/4)/(6-x) = 1/2

 

Multiply by 4(6+x)(6-x) to get:  6-x + 6+x = 2(6-x)(6+x)

 

                                                     12 = 2(36-x²)

 

                                                       6 = 36 - x²

 

                                                      x² = 30

 

                                                      x = √30 = 5.5 mph