SOLUTION: A boat traveled 252 miles downstream and back. the trip downstream took 14 hours. the trip back took 21 hours. what is the speed of the boat in still water? what is the speed of t

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Question 637732: A boat traveled 252 miles downstream and back. the trip downstream took 14 hours. the trip back took 21 hours. what is the speed of the boat in still water? what is the speed of the current?
Found 2 solutions by DrBeeee, solver91311:
Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website!
Use the formula d = rt.
Where d is the distance travelled (miles)
r is the rate of travel (miles/hour)
t is the time of travel (hours)
Downstream your rate is the speed of the boat (b) PLUS the speed of the current (c) for a net speed of (b+c). Upstream the current is "working" against the boat so the net speed is (b-c).
Downstream equation
d = (b+c)*t, applying the given values for the downstream trip yields
(1) 252 = (b+c)*14
Upstream equation
d = (b-c)*t, applying the given values for the upstream trip yields
(2) 252 = (b-c)*21
Now solve (1) and (2) simultaneously
(1) b+c = 252/14 = 18
(2) b-c = 252/21 = 12
Add (1) and (2)
(b+c)+(b-c) = 18 + 12
2b +0 = 30
b = 15
(1) 15 + c = 18
c = 3
Correct? Let's check.
Is (252=(15+3)*14)?
Is (252=18*14)?
Is (252=252)? Yes
Is (252=(15-3)*21)?
Is (252=12*21)?
Is (252=252)? Yes
Answer: The speed of the boat in still water is 15 mph and the speed of the current is 3 mph

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the speed of the boat in still water. Let represent the speed of the current. Downstream the boat travels at miles per hour. Upstream the boat travels at miles per hour.

Distance equals rate times time, so

Downstream trip:

Upstream trip:

Solve the 2X2 system for and

John

My calculator said it, I believe it, that settles it