Math Word Problem? Help!?

Question

A homeowner estimates that it will take her 6 days to roof her house. A professional roofer estimates that he could roof the house in 5 day(s). How long will it take if the homeowner helps the roofer?

It takes a groundskeeper 35 minutes to prepare a softball field for a game. It takes his assistant 40 minutes to prepare the same field. How long will it take if they work together to prepare the field?

Answer 1

First question...

2.727272... days



Second...

18.666666... minutes



Here's how I solved this... Let's assume there are 30 units of work in the first job (I used 30 because 6 x 5 = 30). If it takes the first person 6 days to do it, they're doing it at a rate of 5 units per day. The second person does it at a rate of 6 per day. Working together, they can accomplish 11 units of work per day. Since there were 30 to begin with, 30 / 11 = 2.727272...



Do the same math with the second problem, and you get 18.66666...



A simple formula would be (A * B) / (A + B)

Answer 2

Assuming that the homeowner just helps the roofer and not works alongside, the roofing should take the lesser of the two time periods which is five days.



The second question is different; they work together. You can apply the formula in answer no. 1

Answer 3

The homeowner rate of roofing = 1 roof/6 days

The prof. rate of roofing = 1 roof/5 days



The sum of their rates = (1/6) + (1/5) = 1/2.7



Then, together they will take approximately 2.7 days to finish the roofing.



Similarily for the second problem: The groundskeeper and his assistant will take 18.6 mins to prepare the field.

Answer 4

These jobs are best left to the experts!

I should think the two answers are about 7 days and 45 minutes.

Answer 5

1. 1/x=1/5 +1/6= 11/30, hence x=30/11=2.73 let's say 3 days.



2. 1/x=1/35+1/40, x=18.7 let's say 19 minutes.