a motor boat can go 24 miles downstream in the same amount of time that it takes to go 12 miles upstream. the boats speed in the still water is 12 mph.

Hi Daniel;

*a motor boat can go 24 miles downstream in the same amount of time that it takes to go 12 miles upstream. the boats speed in the still water is 12 mph.*

distance=(rate)(time)

downstream...distance=(speed+current)(time)

upstream...distance=(speed-current)(time)

x=current

24=(12+x)(time)

12=(12-x)(time)

Let's take the second equation and multiply both sides by 2..

2(12)=2(12-x)(time)

24=2(12-x)(time)

24=24

(12+x)(time)=2(12-x)(time)

(time) on both sides cancels...

(12+x)(time)=2(12-x)(time)

12+x=2(12-x)

12+x=24-2x

Let's subtract 12 from both sides...

-12+12+x=24-2x-12

x=12-2x

Let's add 2x to both sides...

2x+x=12-2x+2x

3x=12

x=4

current is 4 miles/hour.