SOLUTION: The time required for the examinees to solve the same problem differs by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem

Question 969588: The time required for the examinees to solve the same problem differs by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve a problem?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The time required for the examinees to solve the same problem differs by two minutes.
Together they can solve 32 problems in one hour.
How long will it take for the slower problem solver to solve a problem?
:
Find how many minutes per problem when they work together, 1 hr = 60 min
60/32 = 1.875 minutes per problem
:
Let t = time required by the slower solver in minutes
then
(t-2) = time required by the faster solver
:
let the completed job = 1, (one problem solved)
:
A shared work equation to solve 1 problem
+ = 1
multiply equation by t(t-2), cancel the denominators, and you have:
1.875(t-2) + 1.875t = t(t-2)
1.875t - 3.75 + 1.875t = t^2 - 2t
3.75t - 3.75 = t^2 - 2t
combine to form a quadratic equation on the right
0 = t^2 - 2t - 3.75t + 3.75
t^2 - 5.75t + 3.75 = 0
using the quadratic formula, a=1; b=-5.75; c=3.75
Two solutions
t = .75, not reasonable
t = 5 minutes a reasonable solution, slower guy per problem
:
:
See if that works out, find how many each can solve in 60 min
We know the faster guy takes 2 min less or 3 min per problem
60/3 = 20 problems
60/5 = 12 problems
--------------------
total: 32 problems
:
Did all this make sense to you? ankor@att.net
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