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.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(39630)   (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
EMPTY_______2r___________________20
Unload____________________
TOTAL_____________________8

The time sum gives you this:

Simplify that:


Multiply by LCD of 2r,
Answer by MathTherapy(10557)   (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 

Time taken to travel 20 miles north, when full is: , or , or 

Time taken to unload cargo: ˝ hr

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

Since total time taken to complete entire trip was 8 hours, then: 

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

S + 120 = 16S 

S – 16S = - 120 

– 15S = - 120

S, or speed of boat, when empty = , or  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/. 

RELATED QUESTIONS


A motorboat heads upstream on a river that has a current of 3 miles per hour.The trip... (answered by josgarithmetic)

Car travels 78 miles in hour and a half. How fast is it going in mph?  (answered by richwmiller)

A train travels at a distances of 100 km and at a speed of 20 km/h. If it had gone two... (answered by TimothyLamb)

A cargo ship travels at a speed of m miles per hour when it is over the open ocean. Which  (answered by Alan3354)

Please help me with this question as soon as possible. 
It takes a train 8 hours to... (answered by ewatrrr)

If a car  travels  1/4 miles in 20 seconds, how fast is it... (answered by Alan3354)

Filling a tank. A water tank has an inlet pip and a drain pipe.  a full tank can be... (answered by stanbon)

A car travels 230 miles in t hours at a speed of r.  If the car travels half as fast but... (answered by oberobic)

A car travels 250 miles in t hours at a speed of  r mph. If the car travels half as fast... (answered by jorel1380)