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

vₓ = 5.5 mile / h and
`v_(y)` = 2.5 mile/h

Step-by-step 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