SOLUTION: The distance between two islands A and B is 36 km. The sea current flows steadily such that a boat can gain a speed of x km/h when it sails from A to B. Mr. Chan sails a boat which

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Question 1112497: The distance between two islands A and B is 36 km. The sea current flows steadily such that a boat can gain a speed of x km/h when it sails from A to B. Mr. Chan sails a boat which takes 1.5 hours to travel from A to B. and then 2 hours from B to A.Find the speed of the boat when there is no sea current.
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Let "u" be the  speed of the boat when there is no sea current, in km/h.

Let "v" be the speed of the current.


Then your "speed" (= "rate") equations are


 = u + v    (1)    (effective speed  with the current)

  = u - v     (2)    ( - - - "  - - -  against the current)


Simplify:

u + v = 24     (3)
u - v = 18     (4)
---------------------Add the equations (3) and (4) to get

2u = 24 + 18 = 42  ====>  u =  = 21.


Then from eq(3)  v =  24 - 21 = 3.


Answer.  The  speed of the boat when there is no sea current  is  21 km/h.

         The speed of the current  is  3 km/h.


Check.   Check it on your own.  It will help you to better understand the problem and the solution.

--------------
It is a typical and standard Upstream and Downstream round trip word problem.

You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site.

Read them attentively and learn how to solve this type of problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems",  the topic "Travel and Distance problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The distance between two islands A and B is 36 km.
The sea current flows steadily such that a boat can gain a speed of x km/h when it sails from A to B.
Mr. Chan sails a boat which takes 1.5 hours to travel from A to B.
and then 2 hours from B to A.
Find the speed of the boat when there is no sea current.
:
let s = the speed of the boat with no current
then
(s+x) = effective speed with the current
and
(s-x) = effective speed against
:
Write a distance equation for each way. dist = time * speed
1.5(s+x) = 36
2(s-x) = 36
simplify both equations divide the first by 1.5, divide the second by 2
s + x = 24
s - x = 18
---------------Addition eliminates x, find s
2s + 0 = 42
s = 42/2
s = 21 km/hr is the speed of the boat in still water
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