If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
Sally can paint 1/4 of a house per hour.
John can paint 1/6 of a house per hour.
Let's say the answer is t hours for the total job.
Then (1/4)t + (1/6)t = 1
(1/4 + 1/6)t = 1
(6/24 + 4/24)t = 1
(10/24)t = 1
t = 24/10 hours = 2.4 hours
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
This is the ans. 2 hours and 24 minutes
But how they work it out?
What don't you understand about Diana's solution?
Here is another way to look at it:
Consider the equation: job = rate x time , or rate = job/time or time = job/rate
sally" rate = job/4
john's rare = job/6
combined rate = job/4 + job/6
= 5job/12
time at that rate = job/(5job/12) = 12/5 - 2.4
From Diana's solution,
2.4 hrs = 2 hrs 24 min
To convert .4 hrs to minutes, multiply by 60.
.4 hrs * 60 min = 24 min
To find out how long it will take for both Sally and John to paint the house together, we can use the concept of work done per unit time.
First, we need to determine how much work is done by Sally in one hour and by John in one hour. We can calculate this by taking the reciprocal of the time taken for each individual to paint the house.
Sally's work per hour = 1 house / 4 hours = 1/4 house per hour.
John's work per hour = 1 house / 6 hours = 1/6 house per hour.
Next, we can add up their individual work rates to find their combined work rate when they work together. So:
Combined work rate = Sally's work per hour + John's work per hour
= 1/4 + 1/6
= 3/12 + 2/12
= 5/12 house per hour.
Now that we know their combined work rate is 5/12 house per hour, we can find the time it takes for them to paint the house together by finding the reciprocal of this combined work rate:
Time taken to paint the house together = 1 / combined work rate
= 1 / (5/12)
= 12/5
= 2.4 hours.
Therefore, it will take Sally and John approximately 2.4 hours to paint the house together.