SOLUTION: 19. A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.Let x = the speed of the boat. Let y

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 19. A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.Let x = the speed of the boat. Let y      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 388652: 19. A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.Let x = the speed of the boat.
Let y = the speed of the current.

a. Write an equation for the motion of the motorboat downstream.
b. Write an equation for the motion of the motorboat upstream.
c. Find the speed of the current.

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.Let x = the speed of the boat.
Let y = the speed of the current.

a. Write an equation for the motion of the motorboat downstream.
d = 48t, d in miles, t in hours
-------------------------------
b. Write an equation for the motion of the motorboat upstream.
d = 32t, d in miles, t in hours
------------------------------------
c. Find the speed of the current.
y = 8 mph
---------------------------
16 miles in 20 mins = 48 mph
16 miles in 30 mins = 32 mph
The boat speed is the average = (48 + 32)/2 = 40 mph
The current is the difference = 8 mph

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat can go 16 miles downstream on a river in 20 minutes. It takes 30 minutes for this boat to go back upstream the same 16 miles.
Let x = the speed of the boat.
Let y = the speed of the current.
a. Write an equation for the motion of the motorboat downstream.
x+y = 16/(1/5) = 80 mph
b. Write an equation for the motion of the motorboat upstream.
x-y = 16/(1/2) = 32 mph
---
c. Find the speed of the current.
Subtract and solve for "y":
2y = 80-32
2y = 48 mph
y = 24 mph (rate of the current)
================
Cheers,
Stan H.