### Math Notes

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##### Topics || Problems

A motor boat can travel 15 miles per hour downstream and 9 miles per hour upstream on a certain river. Find the rate of its current and the rate at which the boat can travel in still water. Solution:

$$V_d = 15 mph$$: Velocity downstream

$$V_u = 9 mph$$: Velocity upstream

$$V_c$$: Velocity of the current

$$V_s$$: Velocity in still water

$$V_d = V_s + V_c$$

$$15 = V_s + V_c$$

$$V_u = V_s - V_c$$

$$9= V_s - V_c$$

By elimination eliminate $$V_c$$

$$24 = 2V_s$$

$$V_s = 12 mph$$

$$V_c = 15-12 = 3 mph$$

Thus the rate of the boat in still water is 12 mph and the rate of the current is 3 mph