It takes Maria 1 1/2 hours to deliver newspapers every morning. Hal can deliver the papers alone in 1 hour. How fast can they deliver the papers if they work together?
How do I set up this problem? Thank you
rate combined=sum of rates= 1trip/1.5hr + 1trip/1hr= 2.5trips/1.5hr
time to deliver= trips/rate= 1.5/2.5=3/5 hr
To set up this problem, we need to find the combined rate at which Maria and Hal are delivering newspapers. We can do this by calculating the rate at which each of them delivers newspapers individually, and then adding their rates together.
First, let's determine Maria's rate. We know that it takes her 1 1/2 hours to deliver newspapers. We can convert this into a rate by taking the reciprocal of the time. In other words, Maria's rate is 1 job (delivering newspapers) divided by 1 1/2 hours:
Maria's rate = 1 / 1 1/2 = 1 / (3/2) = 2/3 jobs per hour.
Now, let's determine Hal's rate. We are told that he can deliver the papers alone in 1 hour, so his rate is 1 job per hour.
To find the combined rate when they work together, we add their individual rates:
Combined rate = Maria's rate + Hal's rate
= 2/3 + 1
= 2/3 + 3/3
= 5/3 jobs per hour.
So, when Maria and Hal work together, they can deliver the papers at a rate of 5/3 jobs per hour. To find out how fast they can deliver the papers, we take the reciprocal of this rate:
Time to deliver papers when working together = 1 / (5/3)
= 1 * (3/5)
= 3/5 hours
Therefore, when Maria and Hal work together, they can deliver the papers in 3/5 hours, which is equivalent to 36 minutes.