I have trouble solving word problems. Can you help me solve this problem?
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take both of them to paint the house together?
Bobpursley already answered your question.
http://www.jiskha.com/display.cgi?id=1226828150
How did you get 10/24 then 24/10?
Remember: when dividing fractions, it is the same as multiplying by the inverse.
s/(b/c)= ca/b
so
1/(10/24)= 24/10
How did you get 10/24? Are you adding the fractions by useing the lease common denominator?
Yes.
Of course! Solving word problems involves breaking down the problem into smaller steps. In this case, we can solve it using the concept of rates.
First, let's determine how much work each person does in one hour. We do this by taking the reciprocal of the time it takes for each person to complete the task:
Sally's rate = 1 house / 4 hours = 1/4 house per hour
John's rate = 1 house / 6 hours = 1/6 house per hour
To find the combined rate of Sally and John working together, we add their rates:
Combined rate = Sally's rate + John's rate
= 1/4 + 1/6
To add fractions, we need to find a common denominator. In this case, it is 12. So we rewrite the fractions with the common denominator:
Combined rate = (6/6) * (1/4) + (4/4) * (1/6)
= 6/24 + 4/24
= 10/24
Now that we have the combined rate, we can find the time it will take both of them to paint the house together. To do this, we divide the work (1 house) by the combined rate:
Time taken = Work / Combined rate
= 1 house / (10/24 houses per hour)
To divide by a fraction, we multiply it by its reciprocal:
Time taken = 1 house * (24/10 houses per hour)
= 24/10 hours
= 2.4 hours
So, it will take Sally and John approximately 2.4 hours to paint the house together.