Question

Julie and Eric row their boats at a constant speed 16 miles Downstream for 2 hours, helped by the current rowing at the same rate, the trip back against the current takes 8 hours. find the rate of the current.

Answer 1

The rate of current is 3 miles/hour

EXPLANATION :

Let x be the rate of the boat

and

y be the rate of the current

The total rate downstream is x + y, since the current is adding a speed to their boat.

The total rate upstream is x - y, since the current is opposite to the direction of the boat.

Note that distance = rate x time

Their trip downstream is 2 hours while in upstream is 8 hours

Since the distance downstream and upstream is the same, we can express it by :

`d=r_1t_1=r_2t_2=16`

Where r1 is the downstream rate with t1 as the time.

r2 is the upstream rate with t2 as the time to go back

r1 = x + y

r2 = x - y

Substitute the values to the formula :

`\begin{gathered} r_1t_1=16 \\ (x+y)*2=16 \\ x+y=8 \end{gathered}`
`\begin{gathered} r_2t_2=16 \\ (x-y)*8=16 \\ x-y=2 \end{gathered}`

Now we have two equations,

Eq 1 : x + y = 8

Eq 2 : x - y = 2

Express Eq 1 as x in terms of y :

x + y = 8

x = 8 - y

Substitute this to Eq 2 :

x - y = 2

(8 - y) - y = 2

8 - 2y = 2

-2y = 2 - 8

-2y = -6

2y = 6

y = 6/2

y = 3