SOLUTION: Suppose a boat has a speed in still water of 10 mph. The boat travels 48 miles upstream and then makes the 48 mile trip downstream, in a total travel time of 10 hours. What is the

Algebra ->  Expressions-with-variables -> SOLUTION: Suppose a boat has a speed in still water of 10 mph. The boat travels 48 miles upstream and then makes the 48 mile trip downstream, in a total travel time of 10 hours. What is the       Log On


   

Question 713149: Suppose a boat has a speed in still water of 10 mph. The boat travels 48 miles upstream and then makes the 48 mile trip downstream, in a total travel time of 10 hours. What is the speed of the river? - (I don't know how to put the info into a table or how to write the equation that would help me figure this out)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose a boat has a speed in still water of 10 mph.
The boat travels 48 miles upstream and then makes the 48 mile trip downstream, in a total travel time of 10 hours.
What is the speed of the river? -
:
Let x = the speed of the river
then
(10-x) = effective speed upstream
and
(10+x) = effective speed downstream
:
Write a time equation; time = dist/speed
:
upstr time + downstr time = 10 hrs
48%2F%28%2810-x%29%29 + 48%2F%28%2810%2Bx%29%29 = 10
multiply by (10-x)(10+x) to clear the denominators, results
48(10+x) + 48(10-x) = 10(10-x)(10+x)
480 + 48x + 480 - 48x = 10(100 - x^2)
960 = 1000 - 10x^2
10x^2 = 1000 - 960
10x^2 = 40
x^2 = 4
x = 2 is the speed of the river
:
:
See if that checks out, find the actual time each way.
48/8 = 6
48/12 = 4
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tot time 10 hr