1. ## Speed of Current

A motorboat can keep a constant speed of 16 mph relative to the water. The boat makea a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?

Let c = speed of current

I know that 20 minutes is 20/60 of an hour or 1/3 of an hour.
I also know that 15 minutes is 15/60 of an hour or 1/4 of an hour.

The formula D = rt is often used in such questions. I also think the formula must somehow be manipulated to show what we are looking for.

D = rt

Upstream = c + 16

Downstream = c - 16

I stuck here.

2. ## Re: Speed of Current

(@ 16-c).........................................>1/3

1/4<..............................................@( 16+c)

1/3(16 - c) = 1/4(16 + c)

HOKAY?
Next step I'd multiply the whole shebang by 12: 4(16 - c) = 3(16 + c) ...no more fractions!

3. ## Re: Speed of Current

4(16 - c) = 3(16 + c)

64 - 4c = 48 + 3c

64 - 48 = 3c + 4c

16 = 7c

16/7 = c

2.2857142857 = c

2.29 mph = speed of current

4. ## Re: Speed of Current

Yep. Usually better to leave as 16/7 = speed of current...

Also, you can check yourself if correct by substituting in original:
4(16 - c) = 3(16 + c)
4(16 - 16/7) = 3(16 + 16/7) ????

5. ## Re: Speed of Current

I did not know that speed can be expressed as fractions.

6. ## Re: Speed of Current

Everything is a fraction: 5 = 5/1

7. ## Re: Speed of Current

Originally Posted by DenisB
Everything is a fraction: 5 = 5/1
Interesting. A lot of students do not know this fact. If a represents any number, then a/1 = any number as well because a divided by 1 = a or any number.