Question

Solve each problem. See Example 2. Callie took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 15 min. If the current in that part of the river is 5 km per hr, what was her boat speed?

Accepted Answer

Define variables: Let $$b$$ represent the boat's speed in still water (in km/hr). The current speed is given as 5 km/hr. Express the effective speeds: When going upstream (against the current), the boat's effective speed is $$b - 5. $$When going downstream (with the current), the effective speed is $$b + 5. $$Convert the given times from minutes to hours: 20 minutes is $$\frac{20}{60} = \frac{1}{3}$$ hours, and 15 minutes is $$\frac{15}{60} = \frac{1}{4}$$ hours. Set up distance equations: Since the distance to the spot is the same both ways, use the formula distance = speed $$	imes$$ time. Let $$d be $$the distance to the spot. Then, $$d = (b - 5) 	imes \frac{1}{3}$$ for upstream, and $$d = (b + 5) 	imes \frac{1}{4}$$ for downstream. Set the two expressions for distance equal to each other and solve for $$b$$: $$(b - 5) 	imes \frac{1}{3} = (b + 5) 	imes \frac{1}{4}. $$Multiply both sides to clear denominators and solve the resulting linear equation for $$b.$$

Solve each problem. See Example 2. Callie took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 15 min. If the current in that part of the river is 5 km per hr, what was her boat speed?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Relative Speed in Upstream and Downstream Motion

Distance, Speed, and Time Relationship

Solving Systems of Equations