A student must leave for campus in 10 minutes or he will be late for class. Unfortunately, he is snowed in. He can shovel the driveway in 18 minutes, and his brother claims to be able to do it in 12 minutes. If they shovel together, how long will it take to clear the driveway? Will this give him enough time for the student to get to the campus?
It will take about ? minutes to clear the driveway together. (type the integer or decimal rounded to one decimal place as needed)
If we consider the act of shovelling the driveway as 1 unit , then
his rate = 1/18 units/min
brother's rate = 1/12
combined rate = 1/18 + 1/12 = 5/36
time at the combined rate = 1/(5/36)
= 36/5 minutes
= 7.2 minutes
To find out how long it will take to clear the driveway together, we can use the formula:
1/time1 + 1/time2 = 1/combined time
Plugging in the values given:
1/18 + 1/12 = 1/combined time
Simplifying:
(12 + 18)/216 = 1/combined time
30/216 = 1/combined time
30combined time = 216
combined time = 216/30
combined time ≈ 7.2 minutes
So, it will take approximately 7.2 minutes to clear the driveway together.
As for whether the student will have enough time to get to campus, we need to consider the total time required to shovel the driveway and the time remaining before the student has to leave.
The student can shovel the driveway in 18 minutes, and there are 10 minutes remaining before he has to leave.
Since 18 minutes is greater than 10 minutes, the student will not have enough time to clear the driveway and get to campus.
To find out how long it will take to clear the driveway together, we need to determine their combined shoveling rate.
The student can shovel the driveway in 18 minutes, so his shoveling rate is 1/18 of the driveway per minute.
His brother can shovel the driveway in 12 minutes, so his shoveling rate is 1/12 of the driveway per minute.
To find their combined shoveling rate, we add the rates together:
1/18 + 1/12 = (2 + 3)/36 = 5/36.
This means that together, they can clear 5/36 of the driveway per minute.
Now we can find out how long it will take them to clear the entire driveway by dividing the total amount of work (1, representing the complete driveway) by their combined shoveling rate:
1 / (5/36) = 36/5 = 7.2 minutes.
Therefore, it will take approximately 7.2 minutes for them to clear the driveway together.
Since the student must leave for campus in 10 minutes, he will have enough time to get to campus after clearing the driveway with his brother.