Students start a business. 1st student builds computer in 18h. Both take 7.2h.How long would it take the second student, working alone, to build the computer?

Question

Two college students have started their own business building computers from kits. Working alone, one student can build a computer in 18 h. When the second student helps, they can build a computer in 7.2 h. How long would it take the second student, working alone, to build the computer?

Answer 1

12 hours.

 

The first student does 7.2/18 of the work when the two students are working together, or 40% of the work. The other student therefore does 60% of the work. Compared to the first student, the second one work 60/40 or 1.5 times faster. Since 18/1.5=12, the second student would complete the computer in 12 hours if he was working by himself.

Answer 2

student #1 takes 18 hours

his rate per hour is 1/18

student #2 takes x hours

his rate per hour is 1/x

together they take 7.2 hours

(1/18)(7.2)+(1/x)(7.2)=1 (job done)

multiply both sides by 18x

(18x)(1/18)(7.2)+(18x)(1/x)(7.2)=18x(1)

7.2x+129.6=18x

129.6=18x-7.2x

129.6=10.8x

x=129.6/10.8

x=12 hours alone for the second student

check:(1/18)x+(1/12)x=1 where x=# of hours together

(36)(1/18)x+(36)(1/12)x=36(1)

2x+3x=36

5x=36

x=36/5

x=7.2 hours together !