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Exercises: The UP Rowing team can row the 18-kilometer portion ofthe Agusan river in 3 hours downstream and 6 hours upstream: How fast is their boat and the rate of...

Question

Exercises: The UP Rowing team can row the 18-kilometer portion ofthe Agusan river in 3 hours downstream and 6 hours upstream: How fast is their boat and the rate of the current of the river?Flying with a tailwind, a plane flew 4200 km in 6 hours. With a headwind, the plane took 7 hours to make the return flight: Find the plane's air speed and the wind speed?

Exercises: The UP Rowing team can row the 18-kilometer portion ofthe Agusan river in 3 hours downstream and 6 hours upstream: How fast is their boat and the rate of the current of the river? Flying with a tailwind, a plane flew 4200 km in 6 hours. With a headwind, the plane took 7 hours to make the return flight: Find the plane's air speed and the wind speed?



Answers

When a plane flies with the wind, it can travel 4200 miles in 6 hours. When the plane flies in the opposite direction, against the wind, it takes 7 hours to fly the same distance. Find the rate of the plane in still air and the rate of the wind.

According to the ocean, we have given data First off, all we let X b duh did Oh, the plane And why be, though read Oh, the ring When the soul in a question We have given information When we use in a question This information there is X plus y is equal to 4200 upon six This is a foster gration and X minus Y is equal to 4200 upon seven This is the second equation When we sold first off all be adding board question There is one and so we have. When we add, we know that we have plus by on minus right there Cancel it'd a We have two x is equal to 4200 up on six plus 4200 of own seven own adding we have two x is equal to 700 plus 600 The value of X comes old there is 1300 on to there is 650 We can say that the value of eggs 650 and then we put duh value off X in equation Fost we have 650 plus why is equal to 4200 upon six on solving we consider there is. Why is equal to 700 minus 650 The venue. Vikram's out, Deary's 50. We can say that the value of X is 650 the value of why is 50 Expedia rate off the plane and Vibe did a radio toe.

We have a boat traveling up and down a stream which is six kilometers long. The stream is flowing at three kilometres per hour down street. The ultimate goal of this problem is to determine how fast our boat could go if it were in perfectly still water. So let's analyze the trip up and down the street. It's on the trip up. We took an amount of time Why and we traveled a distance of six kilometers. So what was our speed? That's the third component of this equation. Well, our speed on still water would be X, but it's lowered by the stream pushing against us. So we have X minus three. Then on our way back down, we would be traveling at X plus three by the same logic that is, the river is helping us along. This is for an amount of time, Z and once again it is six kilometers and finally we have that the total amount of time that we spent sailing, why plus Z was two hours and 40 minutes, which you could also write as about 2.67 hours because we want to have all the same units that is not hours and minutes just hours. With this in mind, let's rearrange itself for X. This is gonna be a lot of algebra here, so just try and keep up, all right? So first off, we need to get our equations so that we can get things in terms of just X. Let's rearrange a couple of our equations and see what we can get. So first off, we're going to take this equation here, and if we rearrange it slightly, we'll get Z is equal to six over X plus three. Then we can plug that into the bottom equation and get why Plus six Over X Plus three equals 2.67 which, with some very simple subtraction, gives why equals 2.67 minus six over X plus three. And so, with that in mind, we can now move on to the final part of this problem, which is absolutely the hardest part as well. We have plenty into the top equation. X minus three times why, which is 2.67 minus six over X plus three and all that is equal to six, and we're going to take this huge, terrifying equation, and we're going to solve it for X. So let's begin. First off, let's distribute these parentheses using the distributive property. Or, as you may have called it, the foil method So it's starting off. Will have 2.67 x minus six X over X plus three. That's just multiplying the acts by the last term here, then minus three times 2.67 which is just eight. And then finally, we have plus because the nigga's will cancel, UM, three times six or 18 over X plus three. Okay, And that is, of course, still equal to six. This is quite a lot to deal with. Let's do some simplifying. We have two terms that are over X plus threes. So let's combine those giving us 2.67 X plus 18 minus six X over X plus three. And then I'm gonna do something kind of interesting here, so you'll understand why in a second I am going to subtract six from both sides. Giving us minus 14 equals zero. That is because negative eight minus six this negative 14. Okay, now, this is a little bit strange looking because there's this X plus three on the bottom. So let's multiply every single term by X plus three. So we will now have 2.67 x times X plus three plus the explodes. Threes will just cancel here, leaving us with 18 minus six x minus 14 times X plus three. And that all equals zero. All right, some distribution ist we done 2.67 x squared, plus three times 2.67 is just eight. So eight x alright, plus 18 minus six x. Those are unaffected minus 14 X and then minus 14 times three, which comes out to 42 and all that is equal to zero. Still, let's combine like terms giving us 2.67 x squared. Now there's, ah, positive eight x and negative six x and a negative. 14 bucks leaving us with a negative 12 x and finally negative 42 positive 18 will combine to give us minus 24. Okay. And that's all equal to zero. Still, that was a lot of tradition. And now we're left with this a quadratic so we can use the quadratic formula to solve this. This is a rather long process. It's painful to work through the entire equation. It takes a long time. So I'm going to spare you all the details of that. I trust that you, on your own consol through the quadratic equation. But if you do so, you will get two different answers. You will get X equals negative 1.5 and X equals six for X equals negative 1.5. Since we're doing the speed, that means we would be moving backwards at 1.5 kilometers per hour. That doesn't make any sense, but X equal. Six That does make sense are resting. Speed is six kilometers per hour, and it was slow down or speed up, depending on the flow of the river. Thus, we have finally figured out that arresting speed would be six kilometers per hour in still water.

According to the ocean, we have given data first. Awful. We let speed oh board in still water. He's eggs long Mito por our we have given that speed off Stream East. Three kilometer per travel. We can say that we have speed. Oh, dream he's three kilometer, but I would and then nets be during upstream we have net speed doing up stream ive equal toe X minus three kilometer per hour and nets booed off Doing Don't stream deary's X plus free kilometer Far our on and then daughter. This tense upstream we have is equal to six. Gilo, Mido and daughter This dense downstream we have If you could do six Gilo medio. We know that Nortel time is equal to this dense are born speed and then the question comes out. Eight. A bone three is equal to six a bone X minus three plus six a bone x close. Three. When we saw this week, wish we have four in tow. X Square minus nine is equal. Dough nine in X plus three plus nine Indo X minus three. When you saw we have four x squared minus Tartus six required oh nine X plus don't be seven plus nine x minus 27. When we saw the new question comes out four X square minus 80 x minus 36 is equal to zero. We take common doing this equation. We have to work square minus nine. X minus 18 is equal to zero. This is 1/4 equation. And we know that when you sold quite a situation, we used aquatic formula aquatic formalize minus B plus minus root B squared, minus four a c. Upon the way, When we use this, we have nine blood miners. The road it the one blessed 1 44 a bone doing Toto Derris for the value of X comes out very six or minus 1.5. We can say that spirit is always positive. There's why X is equal to six. Que lo me don't bar our that is speedboat in string. Water is six kilometre, but our

So we've set up an equation to represent this problem. The Hudson River flows out of three MPH. So on the first trip up river, that means it first over 60 miles speed will be that X, which is the speed in Stillwater minus three and the return trip another 60 miles at X plus three MPH. Three mil, three MPH faster than the speed in Stillwater when we have nine hours total in the trip. So that LCD here will be X minus three times X plus three. And once again, we're going to write out the entire equation, multiplying each side by the LCD. So as we multiply each side here, we can cancel out once we multiply. We have nine X squared minus 81. We're gonna cancel it. The X minus three from the denominator of the first part. In the second term, you can select the X plus three. No multiplying here. Receive. You have 60 times X plus three. This gives us 60 X plus. Eliminating on the X minus three times 60 will give us another 60 X minus 1 80 We're gonna bring everything to the same side. So finally will have nine x squared minus the 60 X and another 60 extra being minus 1 20 x and the 1 80 negative wanted to cancel out. So we just have minus 81 and right away here, receive weaken factor three out in order to get three X squared minus 40 x minus 27. And from here, we're gonna solve with the quadratic formula in order to get a solution for X. So negative B which is negative. Negative. 40 Positive 40 plus or minus Radical B squared times four. We're minus four times a times C so minus four times a 33 x squared times a negative 27 and all of that will be over to a so two times three. And solving this out on a calculator will give us two solutions. One of them will be negative, however, and obviously that doesn't work. You can't go out a negative speed. So the positive answer is X equals 13.98 MPH in Stillwater


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