it takes joh 2 hours to finish working in a yard, mark can work on the same yard for 3 hours. how long will it take both of them if they work as a team?
If it takes them x hours working together, then
1/2 + 1/3 = 1/x
The equation reflects the idea of how much of the job each can do in an hour. Add that up, and it shows how much of the whole job gets done in an hour.
joh = 1 y / 2 h
m = 1 y / 3h
so
(1/2 + 1/3) yard per hour together = 5/6 y/h
(5/6) yards/hr * t hr = 1 yard
t = 6/5 hours
To figure out how long it will take Jo and Mark to complete the yard if they work together, we need to calculate their combined work rate.
Jo can finish the yard in 2 hours, so his work rate is 1/2 of the yard per hour (1 yard / 2 hours = 1/2 yard per hour).
Similarly, Mark can finish the yard in 3 hours, so his work rate is 1/3 of the yard per hour (1 yard / 3 hours = 1/3 yard per hour).
To find their combined work rate, we need to add their individual work rates together: (1/2 yard per hour) + (1/3 yard per hour) = 3/6 + 2/6 = 5/6 yard per hour.
Now, to determine how long it will take them together to finish the yard, we divide the total work required (1 yard) by their combined work rate (5/6 yard per hour):
Time = Total work / Combined work rate
Time = 1 yard / (5/6 yard per hour)
Time = 1 yard * (6/5 yard per hour)
Time = 6/5 hour
Therefore, it will take Jo and Mark 1 hour and 12 minutes (6/5 hours is equivalent to 1.2 hours or 1 hour and 12 minutes) to complete the yard if they work together.