Jack and Jill wash a car at the same rate . Working together it takes them an hour and 10 minutes to wash a car. One day jack started washing a car by himself at 2:30 p m. When he was half way done , Jill joined him . What time did they finish washing the car?
It would take them 70 minutes to wash the whole car working together, working at the same rate.
Jack did half the car by himself , and that would have taken him 70 minutes working alone
so that leaves half the car to be washed by both working together.
This will obviously take them 35 minutes.
so add 70 min + 35 min to 2:30 ----> 4:15 pm
To solve this problem, we need to break it down into smaller parts and calculate the time taken by each person individually.
Let's assume that it takes Jack x hours to wash the car alone. Since Jack and Jill wash a car at the same rate, it will also take Jill x hours to wash the car alone.
We know that when Jack was halfway done, Jill joined him. Therefore, Jack worked alone for x/2 hours, and when Jill joined, they worked together for 1 hour and 10 minutes, which can be converted to (1 + 10/60) hours.
The total time taken by Jack and Jill to finish washing the car is given by:
(x/2) + (1 + 10/60)
According to the problem, Jack started washing the car at 2:30 PM. To find the time they finished, we need to add their total time to the starting time.
Let's convert the starting time to hours for easier calculations. 2:30 PM can be represented as 14:30 in the 24-hour clock format.
Now, adding the total time taken by Jack and Jill to the starting time:
14:30 + [(x/2) + (1 + 10/60)]
To find x, we can use the fact that it takes Jack and Jill together 1 hour and 10 minutes to wash the car:
x + x = 1 + 10/60
2x = 1 + 10/60
2x = 1 + 1/6
2x = 7/6
x = 7/12
Substituting the value of x back into the equation to find the finish time:
14:30 + [(7/12)/2 + (1 + 10/60)]
14:30 + [7/12 * 1/2 + 70/60]
14:30 + [7/24 + 7/6]
14:30 + [7/24 + 28/24]
14:30 + 35/24
Simplifying the fraction:
14:30 + 35/24 = (14 * 24 + 30 + 35)/24 = 365/24
So, they finish washing the car at 365/24 hours after 2:30 PM.
To convert this back to the 12-hour clock format, divide 365 by 24 and find the remainder. The quotient is the number of full 12-hour cycles and the remainder represents the hours.
365 divided by 24 is 15 with a remainder of 5. This means they finish 15 full 12-hour cycles after 2:30 PM, which brings us to 2:30 AM the next day (15 cycles * 12 hours = 180 hours, which is equivalent to 7 days and 12 hours).
Adding the remainder of 5 hours to 2:30 AM, we get the final finish time:
2:30 AM + 5 hours = 7:30 AM.
Therefore, Jack and Jill finish washing the car at 7:30 AM.