SOLUTION: A motorboat travels twice as fast when empty as when it is full. It travels 20 miles north with a cargo,spends half an hour for unloading, and returns to its original port empty,

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A motorboat travels twice as fast when empty as when it is full. It travels 20 miles north with a cargo,spends half an hour for unloading, and returns to its original port empty,       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 895085: A motorboat travels twice as fast when empty as when it is full. It travels 20 miles north with a cargo,spends half an hour for unloading, and returns to its original port empty, taking 8 hours to complete the entire trip. What is the speed of the motorboat when it is empty? Want explanation
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
You made this unclear if the unloading time is part of the trip or if only travel time is part of the trip. My guess is that it is part of the trip and total time.

____________rate_________time________distance
FULL________r____________(___)________20
EMPTY_______2r___________(___)________20
Unload____________________1/2
TOTAL_____________________8

Basic uniform travel rate concept lets us fill in time parts.

____________rate_________time________distance
FULL________r____________20%2Fr________20
EMPTY_______2r___________20%2F%282r%29________20
Unload____________________1%2F2
TOTAL_____________________8

The time sum gives you this:
20%2Fr%2B20%2F%282r%29%2B1%2F2=8
Simplify that:
20%2Fr%2B10%2Fr%2B1%2F2=8
30%2Fr%2B1%2F2=8
Multiply by LCD of 2r,
30%2A2%2Br=16r
60=15r
highlight%28r=4%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

A motorboat travels twice as fast when empty as when it is full. It travels 20 miles north with a cargo,spends half an hour for unloading, and returns to its original port empty, taking 8 hours to complete the entire trip. What is the speed of the motorboat when it is empty? Want explanation


Let speed of motorboat, when empty, be S

Then speed, when it’s full is: ˝S, or S%2F2

Time taken to travel 20 miles north, when full is: 20%2F%28S%2F2%29, or 20+%2A+%282%2FS%29, or 40%2FS

Time taken to unload cargo: ˝ hr

Time taken to travel 20 miles south, when empty is: 20%2FS

Since total time taken to complete entire trip was 8 hours, then: 40%2FS+%2B+1%2F2+%2B+20%2FS+=+8

80 + S + 40 = 16S ----- Multiplying by LCD, 2S

S + 120 = 16S 

S – 16S = - 120 

– 15S = - 120

S, or speed of boat, when empty = %28-+120%29%2F-+15, or highlight_green%288%29 mph

You can do the check!! 



Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.

Further help is available, online or in-person, for a fee, obviously. 



For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL

MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 

Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,

GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.