SOLUTION: . A boat travels at the speed of 20 Miles per hour in still water. It travels 48 miles up stream, and then returns to the starting point in a total of five hours. The speed of the

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: . A boat travels at the speed of 20 Miles per hour in still water. It travels 48 miles up stream, and then returns to the starting point in a total of five hours. The speed of the       Log On


   

Question 17892: . A boat travels at the speed of 20 Miles per hour in still water. It travels 48 miles up stream, and then returns to the starting point in a total of five hours. The speed of the current is ____ miles per hour.
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
let the speed of the boat be x = 20 mph
let the speed of the current be y mph


Then speed up stream = x-y = (20-y) mph
Distance up=48 miles
therefore Time[1] = 48/(20-y)


Speed downstream = x+y = (20+y)mph
Distance=48miles
Time[2]=48/(20+y)


Total time=5 hours
total time=48(20+y)+48/(20-y)
+%2848%2F%2820%2By%29%29%2B%2848%2F%2820-y%29%29=+5+
+%2848%2820-y%29+%2B+48%2820%2By%29%29%2F%28%2820-y%29%2820%2By%29%29+=+5+
+48%2820-y%29+%2B+48%2820%2By%29+=+5%2820-y%29%2820%2By%29+
+2%2A48%2A20+=+5%28400-y%5E2%29+
+%2848%2A40%29%2F5+=+400+-+y%5E2+
+1920%2F5+=+400+-+y%5E2+
+384+=+400+-+y%5E2+
+384-400+=+-y%5E2+
+-y%5E2+=+-16+
+y%5E2+=+16+
Hence y=plus or minus 4
Speed of the current in this context cannot be negative,hence
+y+=+4+


Speed of boat=20 mph
Speed of current=4 mph


Hope this helps,
Prabhat