Question

Ina Crespo rowed 12 miles down the Habashabee River in 1.5 ​hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current.

Answer 1

Answer:

vₓ = 5.5 mile / h  and $v_{y}$ = 2.5 mile/h

Explanation:

This is a problem of adding vectors, but since the canoe and the river are in the same direction, we can make an ordinary sum, write the equations for each situation

I rowed down the river. In this case the speed of the canoe and the river are in the same direction, consequently, they add up

    (vₓ + $v_{y}$) = d / 1.5

I rowed up. In this case the canoe and the river have reversed directions

    (vₓ- $v_{y}$) = d / 4

Feel us two equations with two unknowns,

Let's start by adding the equations

    2vₓ = d / 1.5 + d / 4

    2vₓ = 12 (4 + 1.5) / 4 1.5

    vₓ = 11/2

    vₓ = 5.5 mile / h

Let's substitute in the first of the two equations to find the speed of the river

   (vₓ +$v_{y}$) = d / 1.5

   $v_{y}$ = d / 1.5 - vr

   $v_{y}$ = 12 / 1.5 -5.5

   $v_{y}$ = 8-5.5

  $v_{y}$ = 2.5 mile / h