SOLUTION: A motorboat traveling a distance of 105 miles in 3 hours while traveling with the current. Against the current, the same trip took 7 hours. Find the rate of the boat in calm water

Question 1130533: A motorboat traveling a distance of 105 miles in 3 hours while traveling with the current. Against the current, the same trip took 7 hours. Find the rate of the boat in calm water and the rate of the current.
rate of boat_____mph
rate of current mph

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

x + y = 105/3 = 35 (1) effective speed downstream x - y = 105/7 = 15 (2) effective speed upstream Add the equations. 2x = 35 + 15 = 50 ====> x= 50/2 = 25 miles per hour is the motorboat rate in calm water. ANSWER y= 35 - 25 = 10 miles per hour is the rate of the current. ANSWER

Solved.

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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, where you will find other similar solved problems with detailed explanations.

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 greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Note that you can solve the problem informally, using logical reasoning and some simple calculations, instead of using the formal algebraic approach shown by tutor @ikleyn. The formal algebraic method is certainly valid; but if you just need to solve the problem quickly by whatever method you want (as in a timed mathematics competition), then this alternative method is very useful.

Simple calculations show that the speed of the boat with the current is 35mph while its speed against the current is 15mph.

The 35mph is the boat's speed PLUS the speed of the current; the 15mph is the boat's speed MINUS the speed of the current. Common sense then says that the speed of the boat is halfway between 15mph and 35mph: 25mph. And then the speed of the current is the difference between 25mph and either 15mph or 35mph.

So the speed of the boat is 25mph and the speed of the current is 10mph.
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