In Prairie Dog Creek, Geri can row 60 km downstream in 4 hours or she can row 36 km upstream in the same amount of time. Find the rate she rows in still water and the rate of the c... In Prairie Dog Creek, Geri can row 60 km downstream in 4 hours or she can row 36 km upstream in the same amount of time. Find the rate she rows in still water and the rate of the current.
Understand the Problem
The question is asking to find two unknowns: the rate at which Geri rows in still water and the rate of the current in Prairie Dog Creek. We know her rowing distances downstream (60 km) and upstream (36 km) and the time for both (4 hours). This requires using the formula for speed, distance, and time, allowing us to set up equations to solve for the two rates.
Answer
Geri rows at a rate of $12 \, \text{km/h}$ in still water and the rate of the current is $3 \, \text{km/h}$.
Answer for screen readers
Geri rows at a rate of ( 12 , \text{km/h} ) in still water, and the rate of the current is ( 3 , \text{km/h} ).
Steps to Solve
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Define Variables Let ( r ) be the rate at which Geri rows in still water (in km/h) and ( c ) be the rate of the current (in km/h).
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Set Up Equations for Downstream and Upstream When rowing downstream, her effective speed is ( r + c ). The equation for distance is: $$ \text{Distance} = \text{Speed} \times \text{Time} $$ For the downstream trip: $$ 60 = (r + c) \times 4 $$
When rowing upstream, her effective speed is ( r - c ): $$ 36 = (r - c) \times 4 $$
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Rearrange the Equations First equation becomes: $$ r + c = \frac{60}{4} = 15 $$ Second equation becomes: $$ r - c = \frac{36}{4} = 9 $$
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Combine the Two Equations Now you have two equations:
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( r + c = 15 )
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( r - c = 9 )
Add the two equations: $$ (r + c) + (r - c) = 15 + 9 $$ This simplifies to: $$ 2r = 24 $$
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Solve for ( r ) Divide by 2: $$ r = 12 $$
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Find ( c ) Now substitute ( r ) back into one of the equations: $$ 12 + c = 15 $$ Thus, $$ c = 3 $$
Geri rows at a rate of ( 12 , \text{km/h} ) in still water, and the rate of the current is ( 3 , \text{km/h} ).
More Information
Geri's rowing abilities demonstrate the classic problem of relative speed in currents, a common topic in physics and applied mathematics. Understanding how the current affects speed is vital for navigational skills.
Tips
- Confusing downstream and upstream speeds: It's important to remember that the current aids speed downstream and opposes it upstream.
- Miscalculating the times or distances; reviewing the given information carefully helps avoid errors.
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