Question

Can someone please TEACH this to me. Thanks

Bob can row 10 mph in still water. The total time to travel downstream and return upstream to the starting point is 4 hours and 0 minutes. If the total distance downstream and back is 30 miles, determine the speed of the river (current speed).

Answer 1

i so wish i could use a chalkboard

Answer 2

ok, picture this in your head

Answer 3

the water is flowing at some speed

if the guy doesnt row, then the speed of the boat would be the same as the speed of the river,

right?

Answer 4

yes, but it has the speed of the boat and the speed of the water. doesnt it add up?

Answer 5

we're not at that point yet

Answer 6

ok, so if the river wasnt moving, the problem states, he can row 10mph

Answer 7

ok...

Answer 8

so, if he decided to row with all his strength down river,
his speed relative to the shore would be the speed of the river plus his rowing speed

yes?

Answer 9

yes

Answer 10

ok, now how about if he decided to row with all his might up river?

what would his relative speed be

Answer 11

his speed minus the river speed? or negative

Answer 12

yes

the negative would depend on how you set the x direction
but for teh sake of simplicity, we'll ignore it and use all postive fun numbers

Answer 13

okay

Answer 14

in actuality, the negative speed would cancel out in the problem since you would be traveling a negative distance

Answer 15

so the sign is really, the direction of travel

Answer 16

TOTALLY IRRELEVANT TO THE PROBLEM-sorta

Answer 17

OK, back to the problem

lets define some random variable to be the speed of the river?

any suggestions?

Answer 18

10+x=15(miles)

Answer 19

i mean idk

Answer 20

ok, looks like you decided to use x as the speed of the river

Answer 21

define your variable
write this down--
"Let x be the speed of the river"

Answer 22

ok

Answer 23

now, lets actually look at the problem

Answer 24

total travel time up and down the river is 4 hours
and total distance travelled is 30 miles

from this information, can you tell me how long the river is?

Answer 25

15 miles

Answer 26

very good

Answer 27

ok now we know that the speed going down the river would be
x+10

and he is travelling 15 miles at this speed

so the time it would take to travel this distance would be? (leave answer with variable)

Answer 28

if you still dont know,

distance= speed * time
or if we rearrange the variables
distance/speed = time

Answer 29

uhhh cant solve the problem yet buddy

maybe, but im doing the problem as we go
havent actually solved it or written it down on paper

Answer 30

it would be x+10=15

Answer 31

no,
x+10 is in mph
15 is in miles

mph is not equal to miles

its like trying to compare apples to oranges- one of which would kill me

Answer 32

distance(miles) divided by speed(mph) equals time(hours)

15/(x+10) = time takes to travel down river