SOLUTION: A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?
Algebra.Com
Question 388013: A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat cruises at 15 miles per hour in still water, what is the rate of the current?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Start with the basic formula, Distance equals Rate times Time.
But express it as time as a function of distance and rate:
So let's talk about the downstream trip first. Going downstream the boat goes 15 mph PLUS the rate of the current, i.e. 
, and the 80 mile trip is accomplished in 
hours, so:
Now let's look at the upstream trip. This time the boat speed relative to the shore is 15 mph MINUS the rate of the current, 
, and the 80 mile trip is accomplished in 
hours, so:
A little algebra and fraction addition:
Ah ha! Now we have two things both equal to , so:
Cross-multiply, collect like terms, and put the quadratic into Standard Form.
Factor and solve. Discard the negative root -- unless you can find a river that flows upstream.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat... (answered by Fombitz)
A speedboat takes 4 hours longer to go 80 miles up a river than to return. If the boat... (answered by robertb)
A speedboat takes 1 hour longer to go 24 miles up a river than to return. If the boat... (answered by ptaylor)
an excursion boat takes 1.5 times as long to go 360 miles up a river than to return. If... (answered by lwsshak3)
a speed boat takes 3 hours longer to go 45 miles up a river than to return. if the boat... (answered by lwsshak3)
When Monique rented a boat to a cruise on the Sandy River, she was told that the boat... (answered by uma)
A boat takes 3 hours longer to go 60 miles up a river than to return. If the boat cruises (answered by josmiceli)
a boat takes 2 hours longer to go 45 miles up a river than to return. If the boat's... (answered by Paul,sgt_spike)
Please HELP!
a boat takes 2 hours longer to go 45 miles up a river than to return. If... (answered by venugopalramana)
