May and Bill took 49 hours to complete their History project. They worked separately on their own project. If May had worked 5 hours less and Bill had worked 6 hours more, May would have put in 2 hours more than Bill. How many hours did May put in for the History project?
m+b = 49
(m-5) = 2 + (b+6)
m + b = 45
m - b = 13
2m = 58
m = 29
so, b=16
If May had worked 5 hours less (24), and Bill had worked 6 hours more (22), she'd have put in 2 more hours than Bill.
gotta watch those typos.
m + b = 49
m - b = 13
2m = 62
m = 31
so, b=18
If May had worked 5 hours less (26), and Bill had worked 6 hours more (24), she'd have put in 2 more hours than Bill.
Thank you, Steve! Appreciate your help.
To find out how many hours May put in for the History project, let's represent May's original hours as M and Bill's original hours as B.
According to the given information:
1. May and Bill took 49 hours together to complete the project, so M + B = 49.
2. If May had worked 5 hours less and Bill had worked 6 hours more, May would have put in 2 hours more than Bill. This can be expressed as (M - 5) = (B + 6) + 2.
Now we have a system of equations:
M + B = 49 (Equation 1)
M - 5 = B + 6 + 2 (Equation 2)
To solve this system of equations, we can substitute Equation 1 into Equation 2:
(M + B) - 5 = B + 6 + 2
49 - 5 = B + 8
44 = B + 8
B = 44 - 8
B = 36
Substituting B = 36 into Equation 1:
M + 36 = 49
M = 49 - 36
M = 13
Therefore, May put in 13 hours for the History project.