Question

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?

Answer 1

Formula please!

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

isn't it 5x=25?

Answer 11

yea i screwed up twice. must be early

Answer 12

\[2(25+x)=3(25-x)\]
\[50+2x=75-3x\]
\[5x=25\]
\[x=5\]

Answer 13

sorry. good eye!

Answer 14

can you do one more for me?

Answer 15

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

Answer 16

I just need a formula

Answer 17

sure

Answer 18

yeah since clearly i am unable to solve a linear equation

Answer 19

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.

Answer 20

Find the speed of the boat in still water.

Answer 21

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

Answer 22

again
\[T=\frac{D}{R}\]

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

you can do this better than i can

Answer 27

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

Answer 28

Thanks!!!!!

Answer 29

welcome