Question

PLEASE ME WITH THIS QUESTION YOU GUYS!!!!
Robert can row a boat 1 mile upstream (against the current ) in 20 minutes. He can row the same distance downstream in 10 minutes. Assume that both the rowing and speed of the current are constant. Find the speed at which Robert is rowing and the speed of the current. (you must show all the work in order to obtain credit)

Answer 1

Let s = speed of boat (without the current), c = speed of current

Against current:

d = rt

d = (s-c)t

1= (s-c)(20/60)

60 = 20(s-c)

60/20 = s-c

3 = s - c

3+c = s

s = 3+c

-------------------------

With current:

d = rt

d = (s+c)t

1 = (s+c)(10/60)

60 = 10(s+c)

60 = 10(3+c+c)

60 = 10(3+2c)

60 = 30+20c

60-30 = 20c

30 = 20c

30/20 = c

1.5 = c

c = 1.5

So the current is going 1.5 mph

Answer 2

hello

Answer 3

Let me know if that makes sense or not. Once you get the value of c, use this to find the value of s.

Answer 4

thank you so much

Answer 5

yw

Answer 6

Another approach.
From @jim_thompson5910
"Let s = speed of boat (without the current), c = speed of current"
\[\text{time}=\frac{\text{distance}}{\text{rate}} \]Solve the following for s and c. Elapsed time has been converted from minutes to hours.\[\left\{\frac{20}{60}=\frac{1}{s-c},\frac{10}{60}=\frac{1}{s+c}\right\} \]\[\left\{s=\frac{9}{2}= 4.5\text{ mph},c=\frac{3}{2}=1.5\text{ mph}\right\} \]