Question

Ronald can shovel the driveway in 4 hours, but if his brother Donald helps it would take 2 hours. How long, in hours and minutes, would it take Donald to shovel the driveway alone? (Write your answer in mixed units. Enter a zero in any unneeded blanks.)

Answer 1

Comprehend it <<3

1/4 + 1/t =1/2

4t(1/4 +1/t) = (4t) (1/2)

Therefore t=4, Donald can do the job alone in 4hrs

Answer 2

Ronald can complete the job in 4 hours, so his unit rate is 1/4 of the job per hour. Let x be the unit rate of Donald, i.e. Donald can complete a portion x of the job per hour.

Together, their unit rate is 1/4+x. At this rate, it takes 2 hours to complete the job, meaning that they complete half the job in 1 hour.

So, we have

`(1)/(4) +x=(1)/(2)`⇔
`x=(1)/(2) -(1)/(4) =(1)/(4)`

So, Donald has a unit rate of 1/4, meaning that we would complete the job in 4 hours, too.

NOTE: you could conclude the exercise much quicker: if Ronald alone finishes the job in 4 hour, whereas Ronald and his brother complete the job in half the time, it means that Ronald and Donald's contribution are the same, because the sum of their efforts is exactly twice the effort of Ronald. So, Ronald and Donald must work at the same rate.