My boat go on a trip 56 miles upstream and same distance downstream, has a constant speed 15 miles per hourThe trip can take him 7.5hours Find the speed current

Question

Please find the speed of current with solution 

Answer 1

Let x = speed of the current

 

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

 

Time downstream = 56 / (x+15)

 

Time upstream = 56 / (x-15)

 

Then, 56 / (x+15) + 56 / (x-15) = 15/2

So, 112(x-15) + 112(x+15) = 15(x² - 225)

 

      15x² - 224x - 3375 = 0

 

      x = [224 ± √252676] / 30 = 24.2, or - 9.3

 

Since x can't be negative, x = 24.2 mph