Help with an easy algebra 1 problem?

Question

Please help! Ive got a test in 2 days and I don't understand how to solve this problem.

Mike can build a model airplane by himself in 7 hours. John and mike can do the same job in 5 hours working together. How long would John take to build the plane on his own?

Thanks in advance and I'll be sure to choose a best answer! :)

Answer 1

Mike can build a model airplane by himself in 7 hours.



so, Mike's rate is (1/7) of the job per hour



John can do the job in x hours, or at a rate of (1/x) per hour



when Mike and John work together, they do the same job in 5 hours, or (1/5) of the job per hour.



so, (1/7) + (1/x) = (1/5)



solve for x: (1/5) - (1/7) = (1/x)



[(7 - 5)/35] = 1/x



2/35 = 1/x

2x = 35



x = 17.5



John can build the model in 17.5 hours by himself.



check



id est

Answer 2

Mike can build a model airplane by himself in 7 hours.

John and Mike can do the same job in 5 hours working together.

How long would John take to build the plane on his own?

1/7 + 1/h = 1/5

1/h = 1/5 - 1/7

1/h = 2/35

2h = 35

h = 17.5

John would take 17 1/2 hours to build the plane on his own.

Answer 3

1/7 + 1/J = 1/5

1 represents the whole job, and 1/7 represents rate

1/5 - 1/7 = 1/J

2/35 = 1/J

J = 17.5



John takes 17.5 hours alone, which makes sense because he only makes it 2 hours less , and so he is more than twice as slow as Mike

Answer 4

Let 1/J aircraft/hour be John's rate of work then

5/7 + 5/J = 1 aircraft

5J + 35 = 7J

J = 17.5 hours