SOLUTION: ) Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?

Question 432982: ) Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Lydia takes ten minutes more to complete an illustration than Tom.
The total time taken by both of them is six hours.
How much time did each require?
:
Let's do this in minutes; 6 hrs = 360 min)
:
Let t = time required by Tom alone
then
(t+10) = time required by Lydia alone
:
Let the completed job = 1
:
+ = 1
Multiply by t(t+10), results:
360(t+10) + 360t = t(t+10)
:
360t + 3600 + 360t = t^2 + 10t
720t + 3600 = t^2 + 10t
arrange as a quadratic equation on the right
0 = t^2 + 10t - 720t - 3600
t^2 - 710t - 3600 = 0
Use the quadratic formula to find t
:
The positive solution ~ 715 min for Tom alone
then 725 min for Lydia alone
:
:
This checks out:
360/715 + 360/725 ~ 1
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