SOLUTION: A boat traveled downstream a distance of 95 miles and then came right back. If the speed of the current was 8 mph and the total trip took 6 hours and 20 min, find the average spee

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Question 405959: A boat traveled downstream a distance of 95 miles and then came right back. If the speed of the current was 8 mph and the total trip took 6 hours and 20 min, find the average speed of the boat relative to the water
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A boat traveled downstream a distance of 95 miles and then came right back.
If the speed of the current was 8 mph and the total trip took 6 hours and
20 min, find the average speed of the boat relative to the water
:
Let s = boat speed in still water
then
(s+8) = speed (relative to land) downstream
and
(s-8) = speed upstream
:
Change 6 hr 20 min to 61%2F3 hrs
:
Write a time equation: time = dist/speed
:
95%2F%28s%2B8%29 + 95%2F%28s-8%29 = 61%2F3
change to an improper fraction
95%2F%28s%2B8%29 + 95%2F%28s-8%29 = 19%2F3
:
Multiply by 3(s+8)(s-8), results:
95*3(s-8) + 95*3(s+8) = 19(s+8)(s-8)
:
95(3s-24) + 95(3s+24) = 19(s^2-64)
:
285s - 2280 + 285s + 2280 = 19s^2 - 1216
:
570s = 19s^2 - 1216
:
A quadratic equation
19s^2 - 570s - 1216 = 0
divide by 19
s^2 - 30s - 64 = 0
Factors to
(s+2)(s-32) = 0
The positive solution
s = 32 mph is the boat speed relative to the water
:
:
Confirm this by finding the time for each half of the trip
95/40 = 2.375 hrs
95/24 = 3.958 hrs
------------------
total = 6.333 hrs which is 6 hr 20 min