Algebra Equations

Question

Gab and Van mow the lawn and finishes the job for 40 mins. If gab is twice as fast as Van, how long will it take Gab to finish mowing the lawn if he does the project by himself?

 

My answer was 60 mins. can you help me figure out what the correct answer is?

 

Answer 1

Arthur's answer is correct but i'd also like to point out this problem can be solved with a simple ratio. If both people are working for the same amount of time, and Gab is twice as fast then he's done twice the work. Therefore Gab did 2/3 the work while Van did 1/3. If it takes Gab 40 min to do 2/3 of the work, then it will take him 60 min to do all the work. 40 min/(2/3)=60

If you want to think of it in rates (in minutes per job) then his rate working together is (40 minutes per 2/3 of a job). He has the same rate working alone but the denominator should be 1, so just divide out the (2/3) and you end up with 60min/job.

Answer 2

60 minutes is correct

 

Gab's time=x minutes

Van's time=2x minutes

(1/x)(40)+(1/2x)(40)=1

(1/x)(40)+(1/x)(20)=1

(40/x)+(20/x)=1

60/x=1

60=x

x=60 minutes

check: (1/60)(n)+(1/120)n=1 where n=time it takes both together

2n+n=120

3n=120

n=40 minutes which was stated in the problem