SOLUTION: 1. The sum of three consecutive odd integers is 27. What are the integers? 2. On Wednesday, John drove to school in 45 minutes. On Thursday,he had a test at school so he average

Algebra ->  Linear-equations -> SOLUTION: 1. The sum of three consecutive odd integers is 27. What are the integers? 2. On Wednesday, John drove to school in 45 minutes. On Thursday,he had a test at school so he average      Log On


   



Question 175969: 1. The sum of three consecutive odd integers is 27. What are the integers?
2. On Wednesday, John drove to school in 45 minutes. On Thursday,he had a test at school so he averaged 12 miles per hour more, and it took him 9 minutes less to get to school. How far does he travel to school?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the smallest integer n
The next larger will be n+%2B+2
The next larger will be n+%2B+4
Given:
n+%2B+n+%2B+2+%2B+n+%2B+4+=+27
3n+%2B+6+=+27
3n+=+21
n+=+7
The integers are 7, 9, and 11
-------
d+=+r%2At
Given:
t%5B1%5D+=+3%2F4hr
t%5B2%5D+=+9%2F60hr
In the 1st case,
d+=+r%2A%283%2F4%29
In the 2nd case,
d+=+%28r+%2B+12%29%2A%283%2F4+-+9%2F60%29
d+=+%28r+%2B+12%29%2A%2815%2F20+-+3%2F20%29
d+=+%28r+%2B+12%29%2A%283%2F5%29
The distances are the same in each case, so
r%2A%283%2F4%29+=+%28r+%2B+12%29%2A%283%2F5%29
Multiply each sides by 20
15r+=+12%2A%28r+%2B+12%29
15r+=+12r+%2B+144
3r+=+144
r+=+48 mi/hr
And, since
d+=+r%2A%283%2F4%29
d+=+48%2A%283%2F4%29
d+=+36 mi answer
check answer:
d+=+%28r+%2B+12%29%2A%283%2F5%29
d+=+%2848+%2B+12%29%2A%283%2F5%29
d+=+60%2A%283%2F5%29
d+=+36mi
OK