A positive integer is twice another. The sum of the reciprocals of the two positive integers is . Find the two integers.

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 . Find the two integers.

1st integer = x; {x>0,

2nd integer =2 * (1st integer) = 2x

Given that; 1+1=3

x 2x 14

2+1 = 3 2x 14

3 = 3 2x 14

x=7

Therefore,

1st integer = 7

2nd integer =2*7=14

2. A positive integer is twice another. The difference of the reciprocals of the two positive integers is Find the two integers.

3. Johncan 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  If the total trip took 0.9 hours, then what was his average jogging speed?

4. A bus​ averages 2miles 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 average speed of the bus= x miles⁄hour

A motorcycle is slower, 2 miles⁄hour when considering the bus, Hence, Average speed of a motorcycle= (x-2) miles⁄hour

Bus=165(miles)= x miles⁄hour ∗ t

Motorcycle= 155 (miles)= x(x − 2)

Solving the equation, 155x=165(x-2)

155x =165x -2*165 10x =330

X=33

Therefore, the average speed the bus = x

miles⁄hour

The average speed the bus = 33

Average speed of the motorcycle = (x-2) miles⁄hour = (33-2) miles⁄hour

The average speed of the motorcycle = 31 ?????⁄????

5. Janecan 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?

The total painting work = 1 unit.

Jane can complete the whole work within 7 hours.

In 1 hour, work done by jane = 1/7

Let; her assistant completes the work in time “T” hours.

Therefore in 1 hour, work  doneby her assistant = 1/T

When they both are finishing it together, given that time taken is 3 hours.

In 1 hour, work done by assistant and jane (Both)= 1/3

Therefore 1/T + 1/7= 1/3

1/t=1/3-1/7=7-3/21=4/21

T=21/4

Time taken to finish = 21/4 hours=5.25 hours