A boat travels 20 miles upstream in the same time that it wo

A boat travels 20 miles upstream in the same time that it would take to travel 30 miles downstream. If the rate of the water is 5 miles per hour, find the speed of the boat alone.

Solution

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