Question

Can you check this? Samantha swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 12 minutes. If the river flows at 4 mph, how fast can Samantha swim in still water?

Is it distance = rate * time?

d = 4r * 60t
d = 4r * 12t

I don't know how to find the mph in still water. Also, aren't I supposed to add/subtract something? It's a multiple choice but I don't want to guess wrong.

Answer 1

yes,
Is it distance = rate * time?
thats correct

but when she swims with the overall rate will be SUM of her rate and water

and when she swims AGAINST water, the overall rate will be the difference

makes sense ?

Answer 2

swims with the water***

Answer 3

So when she is going against it, would I change the equation to:
d = -4r * 12t

Answer 4

Wait that doesn't sound right. Do I subtract from something else in the equation?

Answer 5

let take some variables
her rate in still water = r
rate of flow of water = w

so overall rate when she goes with water will be r+w
ok?

Answer 6

and overall rate when she goes AGAINST water will be r-w
got these ?

Answer 7

Oh okay, I understand what you are talking about.

Answer 8

so now again use the equation.,
distance = rate * time
and tell me what u get ?

Answer 9

Would I use these equations?
d = 4 - w * 60t
d = 4 + w * 12t

Answer 10

where does 't' come from ??
t itself =60 in 1st case and 12 in other....


also preferable is to keep 't' in hours
like t=1 in 1st case and t = 12/60 in 2nd

Answer 11

and w = 4

Answer 12

we need to find r

Answer 13

the t was for time

but if i take out the t, all i will have is:
d = r - 4
d = r + 4

Answer 14

see this:
distance = rate * time

for upstream, rate = r-w = r-4
time = 1 (in hours)

so,
d = (r-w)*1

got this ?

can you make an equation for downstream ?

Answer 15

d = (r-w)*1 would be the upstream and
d = (r+w)*12/60 would be the downstream?

Answer 16

correct!
w=4
so can u get the value of r now ?

Answer 17

would she be going at be 6mph?

Answer 18

i mean i got 6 for the r

Answer 19

let me check
60r-240 = 12r+48
48r = 288

yes! r= 6mph :D

Answer 20

awesome, i submitted and it was right! thank you so much for your help!

Answer 21

welcome ^_^