What is the rate of the current?

Question

The steamboat River Queen travels at the rate of 30km/h in still water. If it can travel 45km upstream in the same amount of time that it takes to go 63km downstream, what is the rate of the current?

Answer 1

Let x = rate of the current

 

Speed of boat upstream (against current) = 30 - x

Speed of boat downstream (with current) = 30 + x

 

Distance = (rate)(time), so time = (distance)/(rate)

 

Time upstream = time downstream

 

45/(30 - x) = 63/(30 + x)

 

Cross multiplying, we have:  45(30 + x) = 63(30 - x)

                                           1350 + 45x = 1890 - 63x

                                                       108x = 540

                                                             x = 5

 

ANSWER:  The speed of the current is 5 mph.