Question 204081: Can someone help me solve this word problem?
The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hrs. What is the speed of the boat in still water?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hrs. What is the speed of the boat in still water?
--------------------------
Upriver DATA:
distance = 40 miles ; rate = b-5 ; time = d/r = 40/(b-5) hrs.
--------------------------
Downriver DATA:
distance = 40 miles ; rate = b+5 ; time = 40/(b+5) hrs
---------------------------
Equation:
time up + time down = 6 hrs
---
40/(b-5) + 40/(b+5) = 6
---
Multiply thru by (b-5)(b+5) to get:
40(b+5) + 40(b-5) = 6(b^2-25)
80b = 6b^2 - 150
6b^2 - 80b - 150 = 0
3b^2 - 40b - 75 = 0
(b-15)(3b+5) = 0
Positive solution:
b = 15 mph (speed of the boat in still water)
===============================================
Cheers,
Stan H.
|
|
|
