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?
:
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
:
{{{360/t}}} + {{{360/((t+10))}}} = 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