SOLUTION: It takes a boat 2 hours to travel 28 miles downstream and 4 hours to travel 24 miles upstream. What is the speed of the boat in still water? The boat travels at_____ miles pe

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: It takes a boat 2 hours to travel 28 miles downstream and 4 hours to travel 24 miles upstream. What is the speed of the boat in still water? The boat travels at_____ miles pe      Log On


   

Question 1154015: It takes a boat 2 hours to travel 28 miles downstream and 4 hours to travel 24 miles upstream.
What is the speed of the boat in still water?
The boat travels at_____ miles per hour in still water.
What is the speed of the current of the river?
The speed of the current is ____miles per hour.
Found 3 solutions by josmiceli, MathTherapy, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = speed in still water
Let +c+ = speed of the current
----------------------------------------
(1) +28+=+%28+s+%2B+c+%29%2A2+
(2) +24+=+%28+s+-+c+%29%2A4+
--------------------------------
(1) +2s+%2B+2c+=+28+
(2) +4s+-+4c+=+24+
Multiply both sides of (1) by 2
and add the equations
-------------------------------------
(1) +4s+%2B+4c+=+56+
(2) +4s+-+4c+=+24+
---------------------------
+8s+=+80+
+s+=+10+
and
(1) +2s+%2B+2c+=+28+
(1) +2%2A10+%2B+2c+=+28+
(1) +2c+=+8+
(1) +c+=+4+
----------------------------
speed in still water?
The boat travels at 10 miles per hour in still water.
What is the speed of the current of the river?
The speed of the current is 4 miles per hour.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

It takes a boat 2 hours to travel 28 miles downstream and 4 hours to travel 24 miles upstream.
What is the speed of the boat in still water?
The boat travels at_____ miles per hour in still water.
What is the speed of the current of the river?
The speed of the current is ____miles per hour.
Let speed of boat in still water be S, and speed of current, C

Then overall speed traveling downstream: 

Also, overall speed traveling upstream:  

2S = 20 ----- Adding eqs (ii) & (i)

S, or 

Try and determine the speed of the current on your own!

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Use the given data to find the downstream and upstream speeds:

downstream: 28/2 = 14mph
upstream: 24/4 = 6mph

The 14mph is the speed of the current added to the speed of the boat; the 6mph is the speed of the current subtracted from the speed of the boat.

Logically, that means the speed of the boat is halfway between the 14mph and the 6mph.

So the boat's speed is 10mph; and that makes the speed of the current 4mph.

ANSWERS:
boat speed: 10mph
current speed: 4mph

There are a great number of different kinds of problems where you end up with this kind of situation -- the sum of two numbers is A and the difference of those two numbers is B.

In any situation like that, one of the numbers is the average of A and B; and then the other number is the difference between that average and either of A or B.