Help me Please!!!
Richard can paint a room in two hours and his brother Nick can paint the same room in four hours. How long would it take them to paint the room if they worked together?
let t equal their combined time
each one does some fraction of the job
... t / 2 for Richard
... t / 4 for Nick
they combine to do the whole job ... t/2 + t/4 = 1
2t / 4 + t / 4 = 1 ... 3 t = 4 ... t = 4 /3 ... an hour and 20 minutes
1/2 + 1/4 = 1/t
t = 4/3
To find out how long it would take Richard and Nick to paint the room together, we need to calculate their combined work rate. Let's break it down step by step.
First, let's determine the work rate of each person. Richard can paint a room in two hours, so his work rate would be 1/2 room per hour (1/2 room/hour). Likewise, Nick can paint the same room in four hours, so his work rate would be 1/4 room per hour (1/4 room/hour).
To calculate their combined work rate, we simply add their individual work rates together. So, the combined work rate of Richard and Nick is:
1/2 room/hour + 1/4 room/hour = 2/4 room/hour + 1/4 room/hour = 3/4 room/hour.
Now that we have the combined work rate, we can determine how long it would take them to paint the room together by using the formula: time = work / rate.
In this case, the work would be 1 room (as they need to paint a whole room). So, plugging in the values, we have:
time = 1 room / (3/4 room/hour)
To divide by a fraction, we can multiply by its reciprocal (flipping the numerator and denominator). Therefore:
time = 1 room * (4/3 room/hour) = 4/3 hour.
So, it would take Richard and Nick 4/3 hours to paint the room together, which is equivalent to 1 hour and 20 minutes.
Therefore, working together, Richard and Nick would take 1 hour and 20 minutes to paint the room.