# Debra swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Debra swim if there were no current?

Debra swam 4 kilometers against the current in the same amount of time it took her to swim 12 kilometers with the current. The rate of the current was 2 kilometers per hour. How fast would Debra swim if there were no current?
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Mira Spears
As given rate of current was 2 Km per hour
Let the speed of Debra in still water is u km per hour.
Let the time taken by Debra for swimming 4 km against current =t hours
Time taken by Debra for swimming 12 km with current =t hours also as given it is same
Speed of Debra with current =u+2 km /hour
Speed of Debra against current =u -2 km/hour
$t=\frac{4}{u-2}=\frac{12}{u+2}$
Cross multiplying
$4\left(u+2\right)=12\left(u-2\right)\phantom{\rule{0ex}{0ex}}4u+8=12u-24\phantom{\rule{0ex}{0ex}}32=8u$
u =4 km per hour
Debra 's speed if no current =4 km per hour