SOLUTION: The Speed boat could travel at 5 times the speed of the current. Thus, it could travel 300 miles downstream in 2 hours more than it took to travel 150 miles upriver.What was the sp

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Question 72888This question is from textbook
: The Speed boat could travel at 5 times the speed of the current. Thus, it could travel 300 miles downstream in 2 hours more than it took to travel 150 miles upriver.What was the speed of the boat in still water? This question is from textbook

Found 2 solutions by ankor@dixie-net.com, checkley75:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
he Speed boat could travel at 5 times the speed of the current. Thus, it could travel 300 miles downstream in 2 hours more than it took to travel 150 miles upriver.What was the speed of the boat in still water?
:
Let s = speed in still water:
:
It says,"boat could travel at 5 times the speed of the current."
Therefore the current is 1/5 the speed (.2s)
:
speed upstream: s - .2 = .8s
speed downstream: s + .2 = 1.2s
:
Write a time equations; time = dist/speed:
:
Time to 300 mi downstream = time to go 150 mi upstream + 2 hrs
= + 2
:
Multiply equation by 2.4s, gets rid of the denominator and the decimals:
2(300) = 3(150) + 2(2.4s)
600 = 450 + 4.8s
600 - 450 = 4.8s
:
4.8s = 150
s = 150/4.8
s = 31.25 mph in still water
:
:
Check solution:
Current = .2(31.25) = 6.25 mph
:
Speed upstream: 31.25 - 6.25 = 25 mph
Speed downstream: 31.25 + 6.25 = 37.5 mph
:
300/37.5 = 8 hrs
150/25.0 = 6 hrs
-------------
difference 2 hrs as stated

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
300/(5C+C)=150/(5C-C)+2
300/6C=150/4C+2
50/C=150/4C+2
50/C=(150+8C)/4C
C(150+8C)=50*4C
150C+8C^2=200C
8C^2+150C-200C=0
8C^2-50C=0
C(8C-50)=0
C=0
8C-50=0
8C=50
C=50/8
C=6.25 MPH FOR THE CURRENT SPEED
PROOF
300/6*6.25=150/4*6.25 +2
300/37.5=150/25+2
8=6+2
8=8