Question

Kellen​'s boat travels 15 mph. find the rate of the river current if she can travel 2 mi upstream in the same amount of time she can go 4 mi downstream.​ (let xequalsthe rate of the​ current.)

Answer 1

The rate of the current is 5 mph.

Explanation:

Given : Kellen​'s boat travels 15 mph. If she can travel 2 mi upstream in the same amount of time she can go 4 mi downstream.​

To find : The rate of the river current ?

Solution :

Let x be the rate of the currents .

The downstream speed is 15+x.

The upstream speed is 15-x.

We know that,
`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`

Upstream time = Downstream time

`(2)/(15-x) =(4)/(15+x)`

Cross multiply,

`2(15+x)=4(15-x)`

`30+2x=60-4x`

`6x=30`

`x=(30)/(6)`

`x=5`

Therefore, the rate of the current is 5 mph.

Answer 2

If the speed of the stream is x
Time is given by d/r , where r is the rate and d is the distance;
Rate for upstream = (15-x) mph and that of down stream is (15 +x) mph
The time taken will be the same;
Thus; 2/(15-x) = 4/(15+x)
cross multiplying;
30 +2x = 60 -4x
6x = 30
x =5
Therefore the rate of the river is 5 mph