SOLUTION: It takes Derek 50 minutes to shovel snow from his driveway. When he works with his brother Ken, it takes only 30 min. How long would it take Ken to do the shoveling himself?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Derek 50 minutes to shovel snow from his driveway. When he works with his brother Ken, it takes only 30 min. How long would it take Ken to do the shoveling himself?      Log On


   

Question 524430: It takes Derek 50 minutes to shovel snow from his driveway. When he works with his brother Ken, it takes only 30 min. How long would it take Ken to do the shoveling himself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their individual rates of working to get
their rate working together
In words:
( 1 driveway/Derek's time ) + ( 1 driveway / Ken's time ) = ( 1 driveway/time working together )
Let t = Ken's time to shovel driveway alone
given:
Derek's rate = +1%2F50+
Rate working together = +1%2F30+
----------------------------
+1%2F50+%2B+1%2Ft+=+1%2F30+
Multiply both sides by +150t+
+3t+%2B+150+=+5t+
+2t+=+150+
+t+=+75+
It will take Ken 75 minutes, or 1 hour and 15 min
to shovel the driveway by himself