IM 8.4.9 Lesson: When Are They the Same?

If you were babysitting, would you rather choose?

  • Charge $5 for the first hour and $8 for each additional hour
  • Charge $15 for the first hour and $6 for each additional hour
Explain your reasoning. 

The amount of water in two tanks every 5 minutes is shown in the table.

Describe what is happening in each tank. Either draw a picture in the applet below, say it verbally, or write a few sentences.

Use the table to estimate when the tanks will have the same amount of water.

The amount of water (in liters) in tank 1 after minutes is . The amount of water (in liters) in tank 2 after minutes is . Find the time when the amount of water will be equal.

A building has two elevators that both go above and below ground.

At a certain time of day, the travel time it takes elevator A to reach height in meters is seconds. The travel time it takes elevator B to reach height  in meters is seconds. What is the height of each elevator at this time?

How long would it take each elevator to reach ground level at this time?

If the two elevators travel toward one another, at what height do they pass each other? 

How long would it take?

If you are on an underground parking level 14 meters below ground, which elevator would reach you first?

In a two-digit number, the ones digit is twice the tens digit. If the digits are reversed, the new number is 36 more than the original number. Find the number.

The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 45 less than the original number. Find the number.

The sum of the digits in a two-digit number is 8. The value of the number is 4 less than 5 times the ones digit. Find the number.