A car travels downhill at 72 mph (miles per hour), on the level at 63 mph, and uphill at only 56 mph The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes.
Find the distance between the two towns.
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the average/mean speed is 63.6 (72+63+56/3=63.66666) the formula is: d (distance)= v (vector/speed)x t (time). to get from a-b this is the formula; d(?)=v(63.6)x t(4) which equals 254.4 miles. To get from town b back to town a this is the formula; d(?)=v(63.6) x t(4.6)which equals 292.56.
ReplyDeleteSo, to get from town a-b, the distance is 254.4 miles. to get from b-a it's a distance of 292.56 miles.
Iris
Ps: thank you ms. d for the helpful hint ;)
To find the distance between the towns I decided that there were two different roots because Ms.D never said anything against it. So the root back is under construction and they need to take a forty minute detour.The other rout is regular but both roots are one ways. The distance between the two towns is 360m because 63mx4h=360m.
ReplyDeleteMy answer is that the distance between the 2 towns is 252 miles. I'm unsure about the question though. Is it level in between the towns? If so, Em's answer makes sense because you would multiply 63 (mph) by 4 to get 360. However, since in the question it gives the mph for uphill and downhill as well, then I take it into account that there is a hill. So how I got my answer is that I knew that it took 4 hours to get there, so I could either multiply the uphill mph, the downhill mph or the level mph, because if i just added them up it would take 3 hrs. So, I decided to double the level mph because if I say, doubled the uphill, I would have to double the downhill as well (since it's a hill). I doubled 63 to get 124, then added that to 72 and 56 to get 252. That's how I found the answer for the trip there. However, on the trip back it takes an extra 40 minutes, and it does not say why. I do agree with Em, there could be a construction site and they needed a detour. I'm still working on that answer and probably will think of it...soon. :)
ReplyDeleteSorry if my answer doesn't make much sense I'm not quite clear on the question.
Katty
I'm still working on my answer. (So hard)
ReplyDeleteEveryone,
ReplyDeleteI don't think it's so much the right answer, it's more the process you went through to get that answer. As long as you explain you answer I think that's fine. Also, an answer is better then no answer :)
*Katty*
The distance between each town is 273 miles. The way I found is first I calculated the distance from Town a to b for speeds from 72mph to 56mph. I just multiplied the speed by 4 for 4 hours. Next I did the same thing for going from town b to a but with a different formula: 14/3 x (speed). After that I looked for the same distance between the 2 tables. There were 2 pairs of the same distances between the 2 tables. They were 280 and 266 the speeds were 66.5 mph and 57mph for 266 miles and 60mph and 70mph for 280 miles. Since there was 2 number pairs I found the average of them which was 273 so thats my answer.
ReplyDeleteim working on my answer
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ReplyDeleteIris, it is impossible for A to B to be a shorter journey than B to A. It can be uphill or downhill but both the car travels the same distance.
ReplyDeleteI calculated that the distance between the 2 towns is 273 miles. I figured it out by trial and error in a Excel spread sheet. I broke down the road travel into 3 sections, the first section is downhill from town A to B, the second section is the level section and 3rd section is uphill from town A to B. Since the speeds of 72 mph and 56 mph are both multiples of 8 I think that the juggling between these two sections must be fractions of 0.125 (1/8). At first, I tried each distance, so the first section is 72 mi the second section 126 mi and the third section 56 mi and got a total distance one way of 254 miles. But I found that the travel time from town B back to town A is too short to be 4o minutes. (Difference is 3.81 mins). So next I tried a variety of section distances and finally got this: Section 1: 189 mi, Section 2: 63 mi and Section 3: 21 mi and found a total distance of 273 mi from A to B. And the two times ( Total time from A to B: 240 min, Total time from B to A: 280 min) have a difference of 40 minutes.
ReplyDeletealright well.... my answer is 273mph. this is because the first thing i did was i tried to follow mr. tomali's idea, of a +b, etc. its kind of weird but here's my explanation. i chose this way to do it because itwould make it easier for me to do, and it uses algebra a bit, so i think that would be right.ok, so lets put these mph into letters: 72mph=X, 63mph=y, and 56mph=z. volocity:d/t, and time:d/v. so keep the 4 hours as 4h, and put the 4:40h into 4.67h. a-b is X/72+y/63+z/56=4, and b-a is just X/56+y/63+z/72=4.67(rounded). all the denominators of the fraction are 56,63, and 72. the LCM of all 3 is 504. so now the equasion is: (X/72+y/63+z/56=4)=504(4)and X/56+y/63+z/72=504(4.67)so now it would be something like: (7X+8Y+9Z)=2016, and (9X+8Y+7Z)=2353.68. and all the different bracket number and letter equasion uses addded up are equivilent to 2016+1353.68. so then using those numbers it would become something like: 16X+16Y+16Z=4369.68, then you do 4369.68divded by 16=273.1, and if you round that, it is 273, so thats my final answer: it is 273m between town A and B.
ReplyDelete(i hope that wasen't too hard to understand, sorry)
~Adele~
The distance between town A and town B is 273 miles. I figured out this problem by trying lots of different combinations of uphill, flat and downhill road. I think the correct answer for the way there is: 189 miles of downhill, 63 miles of flat and 21 miles of uphill. The return journey is: 21 miles of downhill, 63 miles of flat and 189 miles of uphill. I turned each section into a decimal representing a part of 4. To do this I divided the amount of time traveled on a certain section by the average speed on that type of ground. For the journey there: (Downhill: 189 divided by 72 = 2.625, level: 63 divided by 63 = 1. Uphill: 21 divided by 56 = 0.375.) 2.625 + 1 + 0.375 = 4. This also works for the return journey,except you use decimals representing parts of 4.667. This is because 4 hours and 40 minutes is 4 and two thirds of an hour. (Downhill: 21 divided by 72 = 0.291666666667, level: 63 divided by 63 = 1, Uphill: 189 divided by 56 = 3.375.) 0.291666666667 + 1 + 3.375 = 4.66666667; or four and two thirds.
ReplyDeleteMy answer is 191M. Now I realize that I didn't calculate any vectors or things like that that I don't understand. I didn't need to because if they traveled 72mph, that's the same distance then going 72 miles at some other time so I just added up all the distances. And on the way back there probobly was traffic so it took them more time.
ReplyDeletei dont even understand the question......
ReplyDeleteSince I felt the question was very hard and i didn't have the time to do it, My answer will have a bunch of flaws. I calculated that the distance is 252 miles because the speed on level ground is 63 mph, which means that in 4 hours the car would have travelled 252 miles. The extra 40 minutes on the return trip was caused by traffic (there was never anything against including this in you answer), and the uphill and downhill sppeeds don't matter.
ReplyDeleteInteresting approach to the question Cooper
ReplyDeleteMy answer is 293.58 because in the question, it never specifies if there are any downhills or uphills therefore I just assumed the whole road was level. I then multiplied 63 (Speed) by 4.66 (4 hours and 40 minutes) which gave me my answer of 293.58.
ReplyDeleteSIncerely, Landon
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ReplyDeleteThe answer is 280 miles. I isolated the unknowns and used different equations to find the answer. I first found the average speed to find the distance. The speeds are 70mph and 60mph
ReplyDeleteOkay so my answer is sort of complicated. The first thinig I did was find the average speed by doing 72+63+56/3= 63.6. Then I converted the time 8.66 hours to find the total travel time. Then I did the average speed (63.6) multiplied by the travel time in hours(63.6 x 8.66) and then I got the total distance there and back (63.6 x 8.66 = 550.776). The total distance was then divided by two to give me the distance between the two towns (550.776/2= 275.388). This assumes that they took the same road there and back and that there was a traffic jam or construction or something slowing them down on the way back.(It says nothing about there NOT being a traffic jam or something) The distance between A and B must be the same as the distance between B and A unless a different route was travelled on the journey to and from the towns.
ReplyDeleteI can't figure it out! I tried for 3h and I still can't find it.
ReplyDeleteIts 278. Not gonna explain right now cuz I'm sick and feel like crap. So every1 get off my back 4 now.
ReplyDeletedosnt really matter what i say, so im gonna try and pretend im smart, k, u guys ready? Assuming that they are not driving in the extreme western area of canada and are driving on the planes, west being the way the sun sets therefore the sun is in their back, making it easier to drive which is why going east the sun blocks your view, you had to miss you exit and had a 40 minute delay.I think the distance between the two towns is 252 because assuming they are just at a normal incline so ya... and thats how liam sees it!
ReplyDeletewell, i guess i shulda said miles, so yes, my answer was in miles....
ReplyDeleteI think that the distance from town A to B is 288m and on the way back it is 280m. SInce this theory does not have much scientific explination, i will make a story to explain my reasoning. Ok so...
ReplyDeleteGrandma and I wanted to go visit my aunt in a nearby town. We set out early in the morning (at 5 to be exact) and encountered very little traffic along the way. My aunts house was great fun, and soon we saw that it was 4 o'clock and decided it was time to go back. So we started heading back, we knew that there would be traffic so we took a shorter route that we thought wouldn't have as much traffic. Unfortunately, there was a lot fo traffic and it took us 40 minutes more to get back than to get there, on the bright side we took 8km less than we did to come here!
That is about as good of an explanation as I could think of but if traffic is valid i think this should be too.
So, from town A to B is 288miles taking a long route, but it takes 4 hours because it is all downhill. From town B to A it is 280miles taking a shorter route which is uphill (because if you go down you have to go back up. well other way but...) you take 4:40hours (which is more time consuming than the other route)but is shorter.
I tried many different possibilities, but I couldn't really answer this question mathematically, so like other people, I had to assume there was traffic. The entire trip was 252m, since all four hours were traveled at the exact same speed, 63 mph. on the way back, it took an extra forty minutes because of traffic.
ReplyDelete