Question

Kelli swam upstream for some distance in one hour. she then swam downstream the same river for the same distance in only 6 minutes. if the river flows at 5 km/hr, how fast can kelli swim in still water? choose the most logical value for the variable to represent. let x = .

1. Kelli can swim at the speed of 55/9 km/hr., that is, x = 55/9 km/hr.
Formulas to know:
• Speed = Distance/Time
• Time = Distance/Speed
• Distance = Speed*Time.
We assume Kelli’s speed to be x km/hr.
The speed of the river is given to be 5 km/hr.
Thus, Kelli’s speed, swimming upstream = (x – 5) km/hr.
Kelli’s speed, swimming downstream = (x + 5) km/hr.
Kelli’s time swimming upstream = 1 hour.
Kelli’s time swimming downstream = 6 minutes = 6/60 hours = 1/10 hours.
Thus, Kelli’s distance swimming upstream = 1(x – 5) km. = (x – 5) km.
Kelli’s distance swimming downstream = (1/10)(x + 5) km.
But, the distance in both cases is constant.
Thus, we get the equation:
(x – 5) = (1/10)(x + 5),
or, 10x – 50 = x + 5,
or, 10x – x = 50 + 5,
or, 9x = 55,
or, x = 55/9.
Thus, Kelli can swim at the speed of 55/9 km/hr., that is, x = 55/9 km/hr.