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Question

Points A and B are on the banks of a river. It takes a motorboat 1 hour to go downstream from A to B and 1 hour 30 min to go up-stream from B to A. How long would it take the motorboat to go from C to D and back, if C and D are on the shores of a lake and the distance between C and D is the same as that between A and B?

Answer 1

On the river, the actual speed of the boat is a combination of how fast the motor can move the boat plus or minus the speed of the current. On the lake, only the motor speed moves the boat. But, we only know information based on the combined speeds of the motor together with or against the current. The problem is to separate these two components.

Speed is expressed as distance divided by time (such as miles per hour). From the problem, we know the motorboat can make 1 trip from A to B with the current in 1 hour. We know, too, that the motorboat can make 1 trip from B to A in 1.5 hours going against the current. With this information we can create two equations for the two unknown speeds:

Let:

M = Speed of the motor

C = Speed of the current

M + C = Combined speed traveling with the current

M - C = Combined speed traveling against the current

Then:

Speed of trip WITH the current =

1 trip / 1 hour = M + C

1 / 1 = M + C

1 = M + C

or

C = 1 - M

Speed of trip AGAINST the current =

1 trip / 1.5 hours = M - C

1 / 1.5 = M - C

0.666667 = M - C

But, from the first equation

C = 1 - M

Therefore:

0.666667 = M - (1 - M)

0.666667 = 2M - 1

2M = 1.6666667

M = 0.8333335

The speed of the motor alone is 1 trip per 0.83333335 hours.

The question asks for the time to make the trip AND back on the lake. So, we need to know the time to make 2 trips. If the motor alone can make 1 trip in 0.833335 hours, then it can make 2 trips in 2 x 0.8333335 hours which equals 1.666667 hours or 100 minutes.

The answer is 100 minutes.

Answer 2

physics...vectors...friction force...gravity...velocity...distance.

can&#039;t help you. i have no idea what you&#039;re talking about.

Answer 3

Do your own homework.  Geez.

Answer 4

wouldn&#039;t it be the same answer???  seeing as motorboats dont really work on shores, and the distance is the same from C-D than from A-B... hope it was the right answer!

and to all of you who are being negative, hellooo, obviously the person tried to find out for theirselves, and that is what yahoo answers is all about.

for a more explanable answer:

OK, so you just add the distance between A and B going upstram and dowstream- 2 hrs and 30 minutes, because the distance is the same from A-B and from C-D. Motorbikes don&#039;t work on shores so those don&#039;t count and we start from the bank.

Try if you can to put that in better words, and there you go (i hope).

Answer 5

Dude that&#039;s so easy.

But to annoy you further I&#039;m not gunna tell you the answer.

Because you should be doing your own Homework not posting on Answers.

Alx

Answer 6

One hour.  No current in a lake.

Answer 7

^ Exactly! :D