## anonymous 5 years ago A boat can go 25 mph in still water. It takes as long to go 160 miles upstream as it does to go downstream 240 miles. How fast is the current?

1. anonymous

2. anonymous

$T= \frac{D}{R}=\frac{160}{25+x}=\frac{240}{25-x}$

3. anonymous

if x = current than rate going up stream is 25-x and rate going down stream is 25+x

4. anonymous

since $T=\frac{D}{R}$ and these times are the same set them equal. then solve as a ratio $160(25-x)=240(25+x)$

5. anonymous

divide both sides by 80 to make life easier $2(25-x)=3(25+x)$ $20-2x=75+3x$ $5x=-50$ $x=-10$ so i probably messed up and x = 10

6. anonymous

oh yes of course. it is $\frac{160}{25-x}=\frac{240}{25+x}$ i had it backwards sorry

7. anonymous

smaller distance over slower rate = bigger distance over bigger rate. my mistake. lets solve this one

8. anonymous

$160(25+x)=240(25-x)$ $2(25+x)=3(25-x)$ $20+2x=75-3x$ $5x=50$ $x=10$

9. anonymous

now we check. if the current is 10 mpr then the rate going up stream is 25-10=15mph . $\frac{160}{15}=10\tfrac{2}{3}$ hours

10. anonymous

isn't it 5x=25?

11. anonymous

yea i screwed up twice. must be early

12. anonymous

$2(25+x)=3(25-x)$ $50+2x=75-3x$ $5x=25$ $x=5$

13. anonymous

sorry. good eye!

14. anonymous

can you do one more for me?

15. anonymous

whew. $\frac{160}{20}=\frac{240}{30}=8$ so trip is 8 hours in either case

16. anonymous

I just need a formula

17. anonymous

sure

18. anonymous

yeah since clearly i am unable to solve a linear equation

19. anonymous

A boat can go 150 miles downstream in the same time it can go 100 miles upstream. The speed of the current is 6 miles per hour.

20. anonymous

Find the speed of the boat in still water.

21. anonymous

same exact eqution as before, only this time the variable will be speed, not current

22. anonymous

again $T=\frac{D}{R}$

23. anonymous

if you put x = speed of the boat then you know that the speed going downstream is x + 6 whereas the speed going up is x - 6

24. anonymous

so time going down is $T=\frac{150}{x+6}$ and time going up is $T=\frac{100}{x-6}$

25. anonymous

set them equal and solve. $\frac{160}{x+6}=\frac{100}{x-6}$

26. anonymous

you can do this better than i can

27. anonymous

typo $\frac{150}{x+6}=\frac{100}{x-6}$

28. anonymous

Thanks!!!!!

29. anonymous

welcome