I need help with a word problem
- Thread starter erin524
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Use this idea to set up your equations.
Name things.
Let x be rate of boat in still water.
Let y be rate of stream
Then x+y is the rate of the boat going downstream.
x-y is the rate of the boat going upstream.
Rate times time = distance.
Set up two equations and solve simultaneously.
If you need further help, show us your work so we can see where the problem is.
Name things.
Let x be rate of boat in still water.
Let y be rate of stream
Then x+y is the rate of the boat going downstream.
x-y is the rate of the boat going upstream.
Rate times time = distance.
Set up two equations and solve simultaneously.
If you need further help, show us your work so we can see where the problem is.
erin524 said:
You're looking for the boat's speed in still water, so it makes sense to choose a variable to represent that quantity.
Let x = boat's speed in still water (in miles per hour)
You are told that the rate of the current is 1 mph.
So, when the boat is traveling DOWNSTREAM (WITH the current), the boat's speed in still water is increased by 1 mph. If the speed of the boat in still water is x mph, then its speed traveling downstream is (x + 1) mph.
Traveling UPSTREAM, the current is working AGAINST the speed of the boat in still water. So, traveling upstream, the boat makes a speed of (x - 1) mph.
If the boat travels a total distance, round trip, of 36 miles, then the distance upstream = distance downstream = 36/2 miles, or 18 miles.
How long does it take the boat to travel 18 miles upstream if its speed upstream is (x - 1) mph? Distance = rate*time, and time = distance / rate.
So, if the distance is 18 miles, and the rate is (x - 1) mph, the time is 18 miles / (x - 1) mph, or 18 / (x - 1) hours
Traveling DOWNSTREAM, you're still covering 18 miles. But going downstream, the rate is (x + 1) mph. And again, time = distance / rate. If the distance is 18 miles, and the rate is (x + 1) mph, the time is 18 miles / (x + 1) mph, or 18/(x + 1) hours.
You're told that the total time for the trip is 15 hours.
Time going upstream + time going downstream = 15 hours
[ 18 / (x - 1)] + [18 / (x + 1) ] = 15
Ok...there's your equation, and the explanation of how you get it.
The ball is in your court now....show us how you'd solve it!
Thank you so much for your replies...but I still can't figure it out. This is what I have:
18/ (x-1) + 18/ (x+1)=15
Then i multiplied both sides by the lcd (x-1)(x+1) and got
15x^2 - 36x - 15 = 0
and now I can't factor it...and we haven't learned quadratic equation yet. Is this possible to factor?
18/ (x-1) + 18/ (x+1)=15
Then i multiplied both sides by the lcd (x-1)(x+1) and got
15x^2 - 36x - 15 = 0
and now I can't factor it...and we haven't learned quadratic equation yet. Is this possible to factor?
You saved me !! No wonder I couldn't solve the problem . . . Thanks so much for all your help!!!