I am trying to study for an exam and one question has me stumped, I should be able to work it out but can't.
Two objects leave a point at the same time, one travelling at 10 m/s and the other at 23m/s an observer sees the first one and then three hours later sees the second. How far away is the origin point?
This should be easy to work out but I just can't get it.
First it is best to get all the units straightened out, so 3 hours = 60 x 60 x 3 = 10800 Seconds
Let the car going 10m/s be A and the one at 23m/s be B
As car A arrives at the point 3 hours after B we know it is 108000m behind (10800 seconds x 10m/s)
Lets let X equal the distance car A has already travelled so at the time t when car B passes the observer we can say they have travelled...
for A, X metres and B X + 108000 metres
Distance = Speed x Time so Time = Distance/Speed
So Car A t = X/10
and Car B t = (X + 108000)/23
As the time for both to reach these respective points is the same we can put both equations equal to eachother so
X/10 = (X + 108000)/23
so
2.3X = X + 108000
1.3X = 108000
X = 83076... metres
Add this to the distance Car B is ahead (108000) and the origin is therefore 191076m (rounded a little)
To check we can see how long it would take each car to cover this distance, for Car A 191076/10 = 19107.6 or 5.3 Hours
And B 191076/23 = 8307... or 2.3 Hours
Thanks Tom, A it makes sence now and B the answer we were supplied is wrong.
Phil
Here is a silly little maths thing, It kept me entertained!
Three men each have ten pounds and decide they want to buy a cow. They each give their ten pounds to a fourth man, the middle man, who goes off to buy a cow. The middle man buys a cow for 25 pounds and decides to keep 2 pounds as commission for his services. He then distributes the remaining three pounds among the three investors, leaving them with 1 pound change each.
Each of the three men has therefore spent 9 pounds and the middle man has kept 2 pounds. 3 X 9 is 27 + 2 = 29 where is the last pound?
There is no extra pound. The cow cost £25 + £2 Commission = £27.
But pedigree livestock is (or was until very recently: I haven't checked) sold in guineas (1 guinea = 21 shillings = £1.05p) and there will also normally be some luck money from the vendor to the buyer, so livestock purchase is much more complicated than you might think!
JimC you are right pedigree cattle are still sold in guineas and you would usually get luck money but generally only at auction