SOLUTION: I need help setting up this problem so I can solve it. Can anyone please help? A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river

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Question 74234: I need help setting up this problem so I can solve it. Can anyone please help?
A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river whose current runs at 5 mph. How far up the river can the boat go and still be back at 12:00 noon?
Thank You!
Found 2 solutions by checkley75, rmromero:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
DISTANCE=RATE*TIME. THE TWO DISTANCES ARE THE SAME THUS WE HAVE:
20X=30(5-X)
20X=150-30X
20X=30X=150
50X=150
X=150/50
X=3 HOURS GOING UP STEAM. THUS 2 HOURS(5-3=2) RETURN DOWN STREAM.
PROOF
20*3=30(5-3)
60=30*2
60=60

Answer by rmromero(383) (Show Source):
You can put this solution on YOUR website!

A motor boat can run 25 mph in still water. The boat starts at 7:00 am going upstream in a river whose current runs at 5 mph. How far up the river can the boat go and still be back at 12:00 noon?

What is asked in the problem?
How far up the river can the boat go and still be back at 12:00noon?
Given:
Rate of motor boat in still water is 25mph
Rate of the current is 5mph
Time ranges from 7:00am to 12:00noon. That's is 5 hours difference.
Representation:
Let x be the distance the boat travel up or down
y = the time it takes the boat to travel upstream
5 - y = the time it takes the boat to travel downstream

rate * time = distance
Upstream 25 - 5 y = x
Downstream 25 + 5 5 - y = x

(25 - 5)y = x eq1
(25 + 5)(5-y) = x eq2
Solve using substitution method
20y = x
30( 5 - y) = x
150 - 30y = 20y
150 = 50y
3h = y this is the time it takes the boat to
travel upstream
5 - y = 5 - 3
= 2 hours --> this is the time it takes the boat to
travel downstream
when y = 3
20y = x
20(3) = x
60m = x This is the distance travel either upstream
or downstream