Let the speed of the boat be #x# #"miles/hour"# and the speed of the current be #y# #"miles/hour"#.

In down stream the trip #(x+y)# #"miles"# takes in #1# hour. so, #825# #"miles"# takes #825/(x + y)# #"hours"#.

Hence, as per question

#825/(x + y) = 33" "" "(i)#

Again, in the trip back, #(x - y)# #"miles"# take #1# hour. Hence #825# #"miles"# take #825/(x - y)# #"hours"#.

Hence, as per question

#825/(x - y) = 55" "" "(ii)#

From equation #(i)#, we get

#825/(x + y) = 33#

or

#x + y = 825/33 = 25" "" "(iii)#

From equation #(ii#), we get

#825/(x - y) = 55#

or

#x - y = 825/55 = 15" "" "(iv)#

Now, solving equations #(iii)# and #(iv)#, we get

#x = 20 and y = 5#

Hence, the speed of the boat is #"20 miles/hours"# and the speed of the current is #"5 miles/hours"#.