Callie took 20 min to drive her boat upstream to water-ski...

Name: Problem 27, Chapter 1: Student's Solutions Manual for College Algebra
Uploaded: 2020-12-30T16:29:32-08:00
Duration: 2 min 47 s
Channel: Sheryl Ezze
Description: 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?

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?

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Key Concepts

Relative Motion in a Fluid Medium

This concept deals with understanding how an object's motion is affected by the moving medium it is in, such as a river or wind. It involves calculating the effective speed by adding or subtracting the speed of the medium from the object's speed in still conditions, which is fundamental in problems involving currents or winds.

Uniform Motion and the Distance-Time Relationship

This concept is based on the idea that if an object moves at a constant speed, the distance traveled is directly proportional to the time spent in motion. This key principle is used to relate time, speed, and distance, allowing the formation of equations that equate equal distances covered under different conditions.

Setting Up and Solving Algebraic Equations

This concept involves translating word problems into mathematical equations that capture the relationships among the given quantities. By equating expressions derived from different scenarios, one can apply algebraic manipulation to solve for the unknown variable, a common technique in many motion and rate problems.

Transcript

00:01 So we have a boat situation.

00:02 We know that the rate of the current is at five kilometers per hour.

00:15 And we don't know the rate of the boat.

00:17 So we want to find the rate of the boat.

00:18 And i'll say that that's the rate of the boat.

00:24 And anytime i have this type of question, i kind of make like a little chart.

00:29 We know that she's traveling at a constant rate with the boat, both upstream and downstream.

00:38 And there's a certain distance, and both these are the same, and we know that there's a rate that's different, or the rate that she inherently is going, and there's a time.

00:49 And we know at a constant that distance will equal rate times time as long as this rate is constant.

00:56 And we know that when she's going upstream, the current is hurting her, as opposed when she's going downstream, the rate is helping her.

01:06 And since we have our speed and hours, kilometers per hour, we want the time to be in that.

01:12 And we knew that this was supposed to be 20 minutes and this was supposed to be 15 minutes.

01:18 But we don't want to use that in terms of minutes.

01:20 We know 20 out of 30, excuse me, 20 out of 60 is going to be one -third of an hour.

01:26 So this will be in terms of hours and this rate will be in kilometers per hour...

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