Question

Micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. He rows back upstream the same distance, against the current, in 0.56 hours. Assuming his rowing speed and the speed of the current are constant, what is the speed of the current?
3 miles per hour
8 miles per hour
11 miles per hour
14 miles per hour

Answer 1

@Michele_Laino

Answer 2

@Blonde_Gangsta

Answer 3

@Michele_Laino Hey do u know how to do this ?

Answer 4

8 or 11mph

Answer 5

8 or 11mph

Answer 6

If I call with v_0 the speed of Micah and with V the speed of the current we can write the subsequent equations:
\[\Large \left\{ \begin{gathered}
\frac{L}{{{v_0} + V}} = 0.32 \hfill \\
\hfill \\
\frac{L}{{{v_0} - V}} = 0.56 \hfill \\
\end{gathered} \right.\]

Answer 7

where L= 4.48

Answer 8

How do u solve that ?

Answer 9

here v_0 is the speed of mica with respect to the water

Answer 10

it is very simple, since those equation compose a system with 2 unknown quantities, so it can be solved with respect to v_0 and V

Answer 11

equations*

Answer 12

can u show me how to solve this plz ?

Answer 13

or do i with me ?

Answer 14

ok!

Answer 15

I can rewrite those equations as below:
\[\Large \left\{ \begin{gathered}
\frac{{4.48}}{{{v_0} + V}} = 0.32 \hfill \\
\hfill \\
\frac{{4.48}}{{{v_0} - V}} = 0.56 \hfill \\
\end{gathered} \right.\]

Answer 16

do i just multiply

Answer 17

so, we have:
\[\Large \left\{ \begin{gathered}
\frac{{4.48}}{{0.32}} = {v_0} + V \hfill \\
\hfill \\
\frac{{4.48}}{{0.56}} = {v_0} - V \hfill \\
\end{gathered} \right.\]

Answer 18

so:
\[\left\{ \begin{gathered}
14 = {v_0} + V \hfill \\
\hfill \\
8 = {v_0} - V \hfill \\
\end{gathered} \right.\]

Answer 19

the first one is 14
the second one is 8

Answer 20

so its either B or D

Answer 21

now, I subtract the second equation, from the first one, so I get:
\[\begin{gathered}
14 - 8 = \left( {{v_0} + V} \right) - \left( {{v_0} - V} \right) \hfill \\
6 = 2V \hfill \\
\end{gathered} \]

Answer 22

what is V?

Answer 23

3

Answer 24

that's right! That's your answer!

Answer 25

OMG your awesome .. Thank you very very much :)

Answer 26

thank you! :)