Solve each problem. See Example 2. Callie took 20 min to drive...

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

Hey, everyone in this video, we're gonna be working through the following problem. Christian wanted to reach home, which was at the center of the sea. He took 15 minutes to maneuver his raft in the opposite direction of the current. On the next day, he took 10 minutes to maneuver, maneuver his raft in the direction of the current. We're asked to find the speed of the Raft. If the speed of the current is two km/h, we're given four answer choices. Option A one kilometer per hour, Option B5 km/h, Option C10 km/h And option D 12 km/h. The first thing we wanna do when we have a word problem like this is just be very clear about the variables we use. OK. When translating this from a word problem into math. So what's what X represent the speed of the raft? All right. So on day one what happens, Christian's maneuvering his raft in the opposite direction of the curve? Ok. So he's traveling upstream, The speed of the current is two km/h. And since he's going in the opposite direction that's gonna work against the speed that he has in his raft. And so the speed is going to be X -2 km/h. Ok. The speed of his raft minus the speed of the current because the current is working in the opposite direction of his speed. No, I recall the relationship between speed, distance and time. We have that the speed V one for day one is equal to the distance D one divided by the time T one. Now, we know that the speed is X - km/h. We don't know the distance he's traveled, do you want? But we know it takes 15 minutes. And so the distance he travels on day one, day 1 is equal to 15 minutes Multiplied by X -2 km/h. All right. So that's what happens on day one. Let's look, look at what happens on day two on day two. Ok. He's going with the current. So the speed is going to be downstream, he's going in the same direction as the current. And so it's going to help him along, it's going to increase his speed. And so the speed that he's moving downstream is gonna be the speed of his raft. X plus the two kilometer per hour speed of the current. Ok. He's going downstream in the direction of that current. It's helping increase his speed. Now again, the relationship between the speed, the distance and the time we have that V two Is equal to D two divided by T two. The speed is X-plus two km/h. OK. And this is equal to the distance he travels on day two D Divided by the time of 10 minutes. OK. So the distance he travels on day two, day 2 is XX plus two kilometers per hour multiplied by 10 minutes. Now, we have an expression for the distance. On day one We have an expression for the distance traveled on day two. Christian's leaving from the same place and going home. So the distance on both days is the same. OK. That means that D one is equal to D two, If we set these equations equal, OK, we have that D1 is equal to 15 minutes Multiplied by XX - km/h. And this is equal to X plus two kilometers per hour, Multiplied by 10 minutes. All right. And now up until this point, you might be wondering why I left the time in minutes and I didn't convert and we're gonna see why we did that here. So we wanna isolate for X. So let's first divide both sides by our 10 minutes. We get 15 minutes Divided by 10 minutes on the left hand side. OK? Multiplied by X minus two kilometers per hour. And that's equal to X plus two kilometers per hour. Now, you'll see that the unit of minute cancels. OK. It divides out. So whether we converted this to seconds hours, it doesn't matter if those units are the same, they'll divide it. So if we weren't setting these equations equal to each other and dividing out, we would have had to make sure that this unit matches with our unit of speed of kilometers per hour. But because we're dividing like this, the minutes divide out and we don't have to worry about converting. So we have 1.5 multiplied by X minus two kilometers per hour is equal to X plus two kilometers per hour. We can expand on the left hand side. We get 1. x -3 km/h Is equal to X-plus two kilometers per hour. OK? Moving all the X terms to the left hand side and the constant terms to the right hand side, We get 0.5 x Is equal to five km/h. And this tells us that X, It is equal to 10 kilometers per hour. So we've found that value of X and now here is where, why it's important to write down at the beginning, what our variables actually represent. OK, we've solved for X. But what is X? OK. After we've done all of that math, it can be hard to remember. In this case, X is the speed of the Raft, which is what we were looking for. So we found that the speed of the raft is 10 km/h, which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you on the next one.

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?

Key Concepts

Relative Speed in Upstream and Downstream Motion

Distance, Speed, and Time Relationship

Setting Up and Solving Algebraic Equations

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