Question 109824
Let r=rate (speed) of the boat with no current
Now we know that:
(r-4)=rate against the current
(r+4)=rate with the current

distance(d)=rate(r) times time(t) or d=rt; t=d/r and r=d/t 

Time required to go 10 miles against the current=10/(r-4)
Time to go 30 miles with the current=30/(r+4)

----And we are told that the above two times are equal.  So our equation to solve:

10/(r-4)=30/(r+4)  multiply both sides by (r-4)(r+4) or cross-multiply and we get:

10(r+4)=30(r-4)  get rid of parens (distributive law)
10r+40=30r-120 subtract 10r from and add 120 to both sides

10r-10r+40+120=30r-10r-120+120  collect like terms

160=20r  divide both sides by 20
r=8 mph-------------------------------boat's rate of speed with no current

CK
10/(8-4)=30/(8+4)
10/4=30/12
10/4=10/4

Hope this helps---ptaylor