Please help me solve this:
Two prisoners have the task of digging a grave in the cemetery.
If working alone, Mr. Samuela can finish the job in 12 hours,
whereas Mr. Jones can complete the same task in 15 hours. What
time of the day would the job be completed if Mr. Samuela starts
working on the job at 7.30am and later joined by Mr. Jones at
10.30am.
Let x = the number of hours after 10:30 that the job will be completed.
We make this chart and fill in the given numbers and x, and 3 hours
from 7:30 to 10:30.
No. of No. of Digging
graves dug hours rate
or fraction of digging in
thereof done graves/hour
Mr. Samuela anytime 1 12
Mr. Jones anytime 1 15
Mr. Samuela 7:30-10:30 3
Both together after 10:30 x
We can fill in the digging rates anytime by dividing 1 grave by the
number of hours:
No. of No. of Digging
graves dug hours rate
or fraction of digging in
thereof done graves/hour
Mr. Samuela anytime 1 12 1/12
Mr. Jones anytime 1 15 1/15
Mr. Samuela 7:30-10:30 3
Both together after 10:30 x
Since Mr. Samuela works at the same rate from 7:30 to 10:30 as he
does anytime, we can fill in his rate for those 3 hours the same.
And when the two work together their combine rate is the sum of their
rates: 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20, we can fill their
combined rate in:
No. of No. of Digging
graves dug hours rate
or fraction of digging in
thereof done graves/hour
Mr. Samula anytime 1 12 1/12
Mr. Jones anytime 1 15 1/15
Mr. Samula 7:30-10:30 3 1/12
Both together after 10:30 x 3/20
Now we can get the fraction of a grave by multiplying the digging
rates times the hours.
No. of No. of Digging
graves dug hours rate
or fraction of digging in
thereof done graves/hour
Mr. Samula anytime 1 12 1/12
Mr. Jones anytime 1 15 1/15
Mr. Samula 7:30-10:30 3/12 3 1/12
Both together after 10:30 (3/20)x x 3/20
Those two fractions of a grave must add up to 1 grave:
3/12 + (3/20)x = 1
1/4 + (3/20)x = 1
Multiply through by 20
5 + 3x = 20
3x = 15
x = 5
So they finished digging the grave 5 hours after 10:30AM which
was 3:30PM.
Edwin