Rebecca
level secondary
parent

1. There are two small holes in the bottom of a tub filled with water. If opened, one hole will empty the tub in three hours; the other will empty it in six hours. If both holes are opened at the same time, how long will it take to empty the tub?
   
   
2. An airplane flies 400 miles per hour in calm air. It can cover 900 miles flying with the wind in the same time that it can cover 700 miles against the wind. What is the speed of the wind?

I would appreciate your help with these problems, so I could maybe help my child.

Both of these problems involve working with rates. For the first problem, water drains through the first hole at the rate of one-third of a tub per hour. Water drains through the second hole at the rate of one-sixth of a tub per hour. Thus if both holes are open then the water drains out at a rate of

For the second problem suppose that the wind speed is x miles per hour. Thus when flying with the wind the airplane travels at 400 + x miles per hour and when flying against the wind it travels at 400 - x miles per hour.

At 400 + x miles per hour the plane will cover 900 miles in

900  ¹/_400 + x hours.

At 400 - x miles per hour the plane will cover 700 miles in

700  ¹/_400 - x hours.

Since these times are equal.

900  ¹/_400 + x = 700  ¹/_400 - x hours.