A motorboat travels a distance of Y kilometers downstream in 3 hours. The boat covers the exact same distance upstream in 5 hours. If the speed of the river current is 4 km/h, what is the value of 2Y?

The correct answer is 120.

Step 1: Define the variables and given values

Let the speed of the motorboat in still water be $v$ km/h.

The speed of the river current is $c=4$ km/h.

The total distance traveled downstream and upstream is $Y$ km.

Step 2: Express downstream and upstream speeds

Downstream speed = $v+4$ km/h

Upstream speed = $v-4$ km/h

Step 3: Formulate equations using Distance = Speed × Time

For downstream travel (Time = 3 hours):

$Y=(v+4)\times 3$

$Y=3v+12$  (Equation 1)

For upstream travel (Time = 5 hours):

$Y=(v-4)\times 5$

$Y=5v-20$  (Equation 2)

Step 4: Solve for the speed of the boat in still water ($v$)

Equating Equation 1 and Equation 2:

$3v+12=5v-20$

Rearranging the terms:

$5v-3v=12+20$

$2v=32$

$v=16$ km/h

Step 5: Calculate the distance $Y$

Substitute $v=16$ into Equation 1:

$Y=3\left(16\right)+12=48+12=60$ km

Step 6: Calculate $2Y$

$2Y=2\times 60=120$

Therefore, the value of $2Y$ is 120.