Question 19122: ollie Carr has just enough money to rent a canoe for 1 1/2 hours. how far out on a lake can he paddle and return on time if he paddles out at 2 km/h and back 4 km/h?
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
Hopefully you've memorized the relationship between distance traveled, rate of speed, and elapsed time:
Distance = Rate * Time
(The asterisk means multiplication.)
Clearly, the distance that Ollie paddles out is the same as the distance he paddles back. What is different are the rates of speed and elapsed time.
Let's call the rate going out r1 and the rate coming in r2. The corresponding elasped times are t1 and t2.
Since the elapsed times must total 1-1/2 hours (3/2 hours), we should solve the equation above for elasped time. This will allow us to write an equation involving the elapsed times.
Divide both sides of the equation above by Rate to solve for Time:
Time = Distance/Rate
The elapsed time going out is:
t1 = d/r1
t2 = d/r2
Now, we can substitute the given values for r1 and r2.
t1 = d/2
t2 = d/4
Since the total time is 3/2, we use the above expressions for the times to write our equation.
d/2 + d/4 = 3/2
Can you solve this equation for d?
Give it a try.
~ Mark
P.S. You should get a distance of 2 miles for your answer.
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