A boy can rake a yard in 2.5 hours, his sister can rake it in 4 hours. How long will it take both of them to rake it?
Reiny answered this.
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In 40 hours, he can rake 16 yards, she can rake 10, so both can rake 26 in 40 hours, or rate=25/40 yards/hr. Reduce that fraction to a decimal.
To find out how long it will take both the boy and his sister to rake the yard, we need to determine their combined rate of work.
Let's find the individual rates of work for the boy and his sister first. The boy can rake the yard in 2.5 hours, so his rate of work is 1 yard / 2.5 hours = 0.4 yards per hour. Similarly, the sister can rake the yard in 4 hours, so her rate of work is 1 yard / 4 hours = 0.25 yards per hour.
To find the combined rate of work, we add the individual rates of work:
Combined rate of work = boy's rate of work + sister's rate of work
= 0.4 yards per hour + 0.25 yards per hour
= 0.65 yards per hour
Now, to find the time it takes both of them to rake the yard, we use the formula:
Time = Work / Rate
Since the work is 1 yard (raking the entire yard) and their combined rate of work is 0.65 yards per hour, we have:
Time = 1 yard / 0.65 yards per hour
Time = 1.54 hours
Therefore, it will take both the boy and his sister approximately 1.54 hours (or about 1 hour and 32 minutes) to rake the yard together.