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 16 minutes, and his brother claims to be al to do it in 14 minutes. If they shovel together, how long will it take to clear the driveway? Will this give enough time for the student to get to the campus?
It will take about
minutes to clear the driveway together.
(Type an integer or decimal rounded to one decimal place as needed.)
Answer
Rounding to one decimal place, it will take approximately \(\boxed{7.5}\) minutes to clear the driveway together.
Step 1 ：Given that the student can shovel the driveway in 16 minutes, his rate of work is \(\frac{1}{16}\) driveways per minute.
Step 2 ：Similarly, the brother can shovel the driveway in 14 minutes, so his rate of work is \(\frac{1}{14}\) driveways per minute.
Step 3 ：The combined rate of work when they shovel together is the sum of their individual rates, which is \(\frac{1}{16} + \frac{1}{14} = 0.13392857142857142\) driveways per minute.
Step 4 ：The time it will take them to shovel the driveway together is the reciprocal of their combined rate, which is \(\frac{1}{0.13392857142857142} = 7.466666666666667\) minutes.
Step 5 ：Rounding to one decimal place, it will take approximately \(\boxed{7.5}\) minutes to clear the driveway together.
