SOLUTION: 1. find three consecutive even integers whose sum is 42. 2. the difference of the squares of the digits of a two digit positive number is 27. If the digits are reversed in or

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Question 161592: 1. find three consecutive even integers whose sum is 42.
2. the difference of the squares of the digits of a two digit positive number is
27. If the digits are reversed in order and the resulting number is subtracted
from the original number, the difference is also 27.what is the original
number?
3.A's rate of doing work is three times of B. On a given day, A & B work together
for 4 hrs.;B is called away and S finishes the rest of the job in 2 hrs. How
long would it take B to do the complete job alone?
4.Peter can run around a 400m tract in 65 sec. How long does it take for John to
run the 400m if he meets Peter in 35 sec.After they start together in a race
around the tract in opposite direction?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1. find three consecutive even integers whose sum is 42.
:
x + (x+2) + (x+4) = 42
3x + 6 = 42
3x = 42 - y
3x = 36
x = 12
:
;
2. The difference of the squares of the digits of a two digit positive number
is 27. If the digits are reversed in order and the resulting number is
subtracted from the original number, the difference is also 27.
what is the original number?
:
Let the number = 10x + y
:
"The difference of the squares of the digits of a two digit positive number
is 27.
y^2 - x^2 = 27
;
"If the digits are reversed in order and the resulting number is
subtracted from the original number, the difference is also 27."
:
10y + x - (10x + y) = 27
10y + x - 10x - y = 27
10y - y - 10 + x = 27
9y - 9x = 27
Simplify, divide equation by 9
y - x = 3
y = (x + 3)
;
Substitute this for y in the 1st equation, find x
(x+3)^2 - x^2 = 27
(x^2 + 6x + 9) - x^2 = 27
x^2 - x^2 + 6x + 9 = 27
6x = 27 - 9
6x = 18
x = 3
Then
y = 3 + 3
y = 6
;
Our number is 36; Check it: 63 - 36 = 27
:
:
3. A's rate of doing work is three times of B. On a given day, A & B work
together for 4 hrs; B is called away and S finishes the rest of the job
in 2 hrs. How long would it take B to do the complete job alone?
:
Where did S come from (a relative perhaps?) I assume you mean A.
:
Let x = time required by A to do the job alone
Then
Let 3x = time required for B to do the job alone. (works 1/3 as fast as A)
:
Let the completed job = 1
:
The given information tells that A worked 6 hrs, and B worked 4 hrs:
:
6%2Fx + 4%2F%283x%29 = 1
Multiply equation by 3x, results
3(6) + 4 = 3x
18 + 4 = 3x
22 = 3x
x = 22%2F3
x = 71%2F3 hrs, A working alone
then
3(71%2F3) = 22 hrs B working alone
:
Check solution on Calc: 6/7.33 + 4/22 = 1.000; confirms our solution
:
:
4.Peter can run around a 400m tract in 65 sec. How long does it take for John
to run the 400m if he meets Peter in 35 sec. After they start together in a
race around the tract in opposite direction? ?
:
When they meet, they will have traveled a total of 400 meters in 35 seconds
:
Find Peter's speed in meters/sec: 400%2F65 = 6.154 m/sec
:
Let s = John's speed in m/sec
:
Write a dist equation; Dist = time * speed
:
35s + 35(6.154) = 400
:
35s + 215.39 = 400
:
35s = 400 - 215.39
:
35s = 184.61
s = 184.61%2F35
s = 5.275 m/sec is John's speed
:
Find time for John to run 400 m:
400%2F5.275 = 75.83 sec to run 400 m
:
:
Check solution:
35 * 5.275 = 184.625 m
35 * 6.154 = 215.39
------------------
Total dist = 400.0
:
Do you have any questions about these?