1) A computer can do 180 000 mathematical operations (such as addition, subtraction, multiplication and division) in one second. If a man can do one of these operations in 12 seconds, how many hours would it take 10 men to do as many operations as one computer would do in 1 second?
2) In a town there are 15 telephones for every 8 people. If there are 26 520 people in this town, how many telephones must be disconnected so that there will be 8 phones for every 15 people?
**Take Note**: Please do not give me algebra and substitution. I would like to know not only the answer, but the process as well. Thanks a lot. 1) For a computer,
1s ->180 000 operations
For a man,
12s -> 1 operations
So for 1 man, find how many operations he can doin 1s,
1s-> 1/12 operations
Thus for 10 men, they can do how many operations per s?
For 10 men,
1s->10/12 operations (cause 10x[1/12] )
Since a computer can do 180 000 operations in 1s, so how long would it take 10 men to do 180 000 operations?
?s -> 180 000qns
To calculate ?s,
divide 180 000 by 10/12, hence the answer is 216 000s, which then can be converted to 60 hours.
As for qns 2,
You want to achieve
8 phones -> 15 pple
which means,
1 phone -> 15/8 pple
Taking note that there are 26 520 pple in the town and
15 telephones -> 8 pple (given)
You can deduce
1 telephone -> 8/15 pple
so for 26520 pple, how many telephones are there?
? telephones -> 26520 pple
Calculate ? by using 26520 divided by 8/15. Thus ? is .
Hence,
49725 telephones -> 26520 pple
This isn't your answer yet.
Calculate how many phones are needed for 26520 pple so that 8 phones can be for 15 pple.
Using the relationship we have established previously that is the requirement of the qns,
1 phone -> 15/8 pple
x phones -> 26520 pple
calculate x. It is 14144.
Subtract x from ?, ie. 49725 - 14144 to obtain the ans. Therefore,
35581 telephones must be disconnected so that there will be 8 phones for every 15 people.
I'm not too sure about the 2nd qns, hope I didn't confuse you. But the 1st qns should be quite clear I hope. sounds like an SAT problem.. Good luck! Trying makes you learn a lot. 2)
Right now, there are
(15/8)(26520) = 49725 phones
We want:
(8/15)(26520) = 14144 phones
So we need to disconnect:
49725 - 14144 = 35581 phones 1) 1 men do 1 operation so 10 men do 10 operation
10unit is 180000
1 unit is 18000
time taken = 18000*12
=216000sec
=60h
2) 26520 / 8= 3315
3315 *15=49725
26520/15=1768
1768*8=14144
difference is 35581. phone need to be disconnected is 35581 1)speed computer= 180000 operations/sec
speed man= 1operation in 12 seconds=(1/12)operations/sec
speed 10 men=10*speed one man=(10/12) operations/sec
number of hours=speed computer/speed 10 men
= 180000/(10/12)=60 hours
2)8 people have 15 lines then 26520 will have 49725 lines.
but we need 15 people to have 8 lines then 26520 will need 14144 lines.
so the number of lines to be disconnected is equal
49725-14144=35581
please check answers again for possible missed calculations.
good luck. 1)
1 man 1 operation 12 seconds
1 man 180000 operations 180000x12=2160000 seconds
1 man 2160000 seconds
10 men 2160000/10=216000 seconds=
216000/3600 hours=
60 hours
2)
8 people 15 phones
26520 people 26520x15/8 = 49725 phones
15 people 8 phones
26520 people 26520x8/15 = 14144 phones
49725 - 14144 = 35581 phones to be disconnected | 