Question 142297

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let r= rate of the boat in still water
r-5=rate of the boat upsteam 
r+5=rate of the boat downstream

Time to travel upstream=20/(r-5)
Time to travel downstream=30/(r+5)

Now we are told that the above two times are equal, so:

20/(r-5)=30/(r+5) multiply each term by (r-5)(r+5) or cross-multiply and we get:

20(r+5)=30(r-5)  get rid of parens

20r+100=30r-150  subtract 30r and also 100 from each side
20r-30r+100-100=30r-30r-150-100  collect like terms

-10r=-250  divide each side by -10

r=25 mph-----rate of boat in still water

CK

20/(25-5)=30/(25+5)
20/20=30/30
1=1


Hope this helps---ptaylor