I have trouble solving word problems. Can you tell me the best approach to solve this word 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 for both of them to paint the house together?

What is the rate of each working?

Sally=house/4hrs
John=house/6hours

combined rate= Sally rate + john rate
= house(1/4 + 1/6)=house (10/24)

housetogether=combindedrate(time

time=house/house(10/24)=24/10=2.4 hrs.

Certainly! To solve this word problem, we can use the concept of rates. The rate at which someone can do a task is the reciprocal of the time it takes to complete the task.

First, let's find the rates of Sally and John's painting. Sally can paint the house in 4 hours, so her painting rate is 1 house per 4 hours, or 1/4 houses per hour. Similarly, John can paint the house in 6 hours, so his painting rate is 1/6 houses per hour.

To find the combined rate of Sally and John working together, we can add their individual rates. So, the combined rate is (1/4) + (1/6) houses per hour.

Now, we can calculate the time it will take for both of them to paint the house together by taking the reciprocal of the combined rate. In other words, we divide 1 by the combined rate.

To do this, we can find a common denominator for 4 and 6, which is 12. Then, we convert the fractions:

(1/4) + (1/6) = (3/12) + (2/12) = 5/12

So, the combined rate is 5/12 houses per hour.

Now, we take the reciprocal of 5/12 to find the time it takes for both of them to paint the house together:

1 / (5/12) = 12/5

Therefore, it will take Sally and John 12/5 hours, or 2.4 hours, to paint the house together.

So, to solve this word problem, we used rates and the concept of reciprocal to find the combined painting rate and then determined the time it would take for both Sally and John to complete the task together.