Unit 5 Problems
Application problems including rational equations.
Set up a rational equation and then solve the following problems.
1. A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14 . Find the two integers.
let one integer = x
other integer = 2x
sum of reciprocal = 1/x + 1/2x=3/14
=> 3x/3=21/3
=> x = 7
one no. = 7
other no. = 14.
2. A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18 Find the two integers.
Let one of the integer be x
The other is 2x.
1/x-1/2x=1/18.
Multiply through by18x:
18-9=x so x=9.
The two integers are 9 and 18.
3. John can jog twice as fast as he can walk. He was able to jog the first 5 miles to his grandmother's house, but then he tired and walked the remaining 2 miles. If the total trip took 0.9 hours, then what was his average jogging speed?
:
Let x = his jogging speed
2x = his walking speed
write a time equation, time = dist/speed
jog time + walk time = 0.9 hrs
5/x+2/2x=9/10
50+10=9x
x = 6.67
John’s jogging speed is therefore 6.67 miles/hr.
4. A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?
Let the speed of motorcycle be x
Speed of the bus = x+2
165/(x+2)=155/x
165x=155x+310
X=31
Hence: the speed of the motorcycle is 31 Miles/Hour
Speed of the bus is x+2=31+2 = 33 Miles/Hour.
5. Jane can paint the office by herself in 7 hours. Working with an associate, she can paint the office in 3 hours. How long would it take her associate to do it working alone?
Let the time taken by associate alone be x.
Therefore;
1/7+1/x=1/3
Multiply all through by 21x
3x+21=7x
21=4x
X=21/4hrs
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