SOLUTION: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. work

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. work      Log On


   

Question 906274: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes a paint the entire house. working together, they can complete the job in 6 hours.
1. If Mark can finish the job in m hours, how long will it take Jessie to finish the job?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Jessie and Mark are planning to paint a house together. Jessie thinks that if he
works alone, it would take him 5 hours more than the time Mark takes a paint the
entire house. working together, they can complete the job in 6 hours.
1. If Mark can finish the job in m hours, how long will it take Jessie to finish
the job?

Mark can finish the job in m hours
Then Mark's rate is "1 job per m hours" or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cm%2Chours%29 or matrix%281%2C2%2C1%2Fm%2Cjob%2Fhr%29

Jessie thinks that if he works alone, it would take him 5 hours more than
the time Mark takes a paint the entire house.
So Jessie thinks it would take him m+5 hours.

Then Jessie's rate is "1 job per m+5 hours" or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2Cm%2B5%2Chours%29 or matrix%281%2C2%2C1%2F%28m%2B5%29%2Cjob%2Fhr%29

working together, they can complete the job in 6 hours.
So their combined rate is "1 job per 6 hours" or matrix%281%2C2%2C1%2Cjob%29%2Fmatrix%281%2C2%2C6%2Chours%29 or matrix%281%2C2%2C1%2F6%2Cjob%2Fhr%29

Just like those problems where we ADD the boat's rate to rate of the river,
we ADD the two boy's rates to find their combined rate.  So we get the
equation from

%28matrix%285%2C1%2C%22Mark%27s%22%2Cwork%2Crate%2Cin%2Cjob%2Fhr%29%29%22%22%2B%22%22%28matrix%285%2C1%2C%22Jessie%27s%22%2Cwork%2Crate%2Cin%2Cjob%2Fhr%29%29 %22%22=%22%22 %28matrix%286%2C1%2CTheir%2Ccombined%2Cwork%2Crate%2Cin%2Cjob%2Fhr%29%29

1%2Fm%22%22%2B%22%221%2F%28m%2B5%29 %22%22=%22%22 1%2F6

Solve that.  It will take Mark 10 hours and Jessie 5 hours longer
or 15 hours.

Edwin