Answer:
16 hours
Explanation:
From the above question, we are given the following information
For one wall, working alone,
Amy can paint for 12 hours
Which means, in
1 hour , Amy would have painted = 1/12 of the wall
Bob can paint for 18 hours
Which means ,
in 1 hour, Bob would have painted = 1/18 of the wall.
We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.
Step 1
Find the portion of the wall Amy painted before Bob took over.
Amy painted the wall for 4 hours before Bob took over.
If:
1 hour = 1/12 of the wall for Amy
4 hours =
Cross multiply
4 × 1/12 ÷ 1
= 4/12 = 1/3
Amy painted one third(1/3) of the wall
Step 2
Find the number of hours left that Bob used in painting the remaining part of the wall
Let the entire wall = 1
If Amy painted 1/3 of the wall
Bob took over and painted = 1 - 1/3
= 2/3 of the wall
If,
Bob painted 1/18 of the wall = 1 hour
2/3 of the wall = ?? = Y
Cross multiply
2/3 × 1 = 1/18 × Y
Y = 2/3 ÷ 1/18
Y = 2/3 × 18/1
Y = 36/3
Y = 12 hours.
This means, the number of hours Bob worked when he took over from Amy = 12 hours.
Step 3
The third and final step is to calculate how many hours it took them to paint the wall
Number of hours painted by Amy + Number of hours painted by Bob
= 4 hours + 12 hours
= 16 hours
Therefore, it took them 16 hours to paint the entire wall.