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

Answer:

The rate of the current is 5 mph.

Step-by-step 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

$\frac{2}{15-x} =\frac{4}{15+x}$

Cross multiply,

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

$30+2x=60-4x$

$6x=30$

$x=\frac{30}{6}$

$x=5$

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