John can type two-thirds of a paper in 8 hours. If Laura joins him, they can complete the typing in 4 hours. The number of hours Laura would take to type the paper alone would be ????
2006-10-12 12:31:36 · 7 answers · asked by britiani j 1 in Science & Mathematics ➔ Mathematics
This is a horrible question for a teacher to assign. They may not type at the same speed, so there's no way to know for sure.
2006-10-12 12:35:13 · answer #1 · answered by A W 4 · 0⤊ 0⤋
Let x be the portion of the job that John would do (i.e. half the job means x=0.5). Then the portion that Laura would do is 1-x.
The time taken by both of them is
rx = s(1-x) = 4.
where r is John's rate and s is Laura's rate, in papers per hour. We know that r=8/(2/3)=12, and s is unknown.
That means x=4/12 =1/3, so John did 1/3 of the work and Laura did 1-x=2/3. From s*(1-x)=4, we find s=4/(2/3)=6, so Laura would complete the paper in 6 hours.
2006-10-12 19:41:02 · answer #2 · answered by James L 5 · 0⤊ 0⤋
Let J= John's rate (2/3)/8=2/24=1/12 hr^-1
Let L=Laura's rate
given J+L=1/4 hr^-1
L=J+L-J=1/4-1/12=3/12-1/12=2/12=1/6
so Laura can type the paper in 6 hrs
2006-10-16 16:51:31 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋
in 1 hour John can type 1/12 paper
4*1/12+4*x=1
4x=2/3
x=1/6
laura would take 6 hours
2006-10-12 19:36:12 · answer #4 · answered by raj 7 · 0⤊ 0⤋
Do your own work!
2006-10-12 19:33:05 · answer #5 · answered by katlover118 2 · 0⤊ 0⤋
2 hours!!!!!!
2006-10-12 19:36:57 · answer #6 · answered by Anonymous · 0⤊ 0⤋
six hrs
2006-10-12 19:32:51 · answer #7 · answered by Cold Hard Fact 6 · 0⤊ 0⤋