Question

kelli swam upstream for some distance in one hour.she then swam downstream for the same distance in only 6 minutes. if the river flows at 5 km/hr, how fast can kelli swim in still water?

Answer 1

C, A, B, 6.11

Explanation:

A. Kelli's swimming speed in still water

B. 1 (x- 5)

C. 0.1 (x+ 5)

D. 6.11 km/hr

Answer 2

6.11 km/hr

Explanation:

We will use the distance equation:
`D=rt`

Where D is distance (in km), r is the speed/rate (in km/hr), and t is the time taken (in hours)

• The rate going downstream is with the current, so rate is r+c
• The rate going upstream is against the current, so rate is r-c

where c is current rate (river flow rate)

kelli swam upstream for some distance in one hour:

We can write
`d=(r-c)(1)\\d=r-c`

she then swam downstream for the same distance in only 6 minutes:

* note 6 minutes in hours is
`(6)/(60)=(1)/(10)`hr

We can write
`d=(r+c)((1)/(10))\\d=(1)/(10)r+(1)/(10)c`

Since the river flows at 5km/hr, c is 5 and total distance is equal, so we can equate the distance and solve for r:

`r-c=(1)/(10)r+(1)/(10)c\\r-5=(1)/(10)r+(1)/(10)(5)\\r-(1)/(10)r=(1)/(10)(5)+5\\(9)/(10)r=(1)/(2)+5\\(9)/(10)r=(11)/(2)\\r=((11)/(2))/((9)/(10))\\r=(11)/(2)*(10)/(9)=(110)/(18)=6(1)/(9)`

In decimal, 6.11 km/hr. This is Kelli's speed in still water.