SOLUTION: A motorboat can travel at a rate of 15 mph in still water. It went downstream on a river in 4 hours. It took 6 hours to return the same distance. What is the rate of the current. H

Algebra ->  Human-and-algebraic-language -> SOLUTION: A motorboat can travel at a rate of 15 mph in still water. It went downstream on a river in 4 hours. It took 6 hours to return the same distance. What is the rate of the current. H      Log On


   

Question 5891: A motorboat can travel at a rate of 15 mph in still water. It went downstream on a river in 4 hours. It took 6 hours to return the same distance. What is the rate of the current. How far did the boat go?
My answer was: Rate of current -30
The boat went 150 miles
Is this right? Thanks!
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the current
rate with the current = 15+x
rate against the current = 15-x
distance both ways is equal
rate * time = distance
distance going=(15+x)4
distance coming = (15-x)6
set these equations equal to one another because distance both ways is equal:
(15+x)4=(15-x)6
60+4x=90-6x
subtract 60 from both sides
4x=30-6x
add 6x to both sides
10x=30
divide both sides by 10
x=3
the current = 3mph
(15+3)4= distance
18*4 = distance
72 miles = distance
verify:
(15-3)*6 = distance
12*6 = distance
72 miles = distance
The boat traveled 144 miles total in a 3 mph current