Question

The Jacksons and the Simpsons were competing in the final leg of the Amazing Race, which was 240 kilometers long. In their race to the finish, the Jacksons immediately took off traveling at an average speed of v kilometers per hour. The Simpsons' start was delayed by an hour. When they eventually took off, they traveled at an average speed that was 40 kilometers per hour faster than the Jacksons' speed. Sadly for them, that didn't help, and the Jacksons won. Write an inequality in terms of v that models the situation.

Answer 1

To model the race situation as an inequality, the time taken by the Jacksons (240/v) must be less than the sum of the time taken by the Simpsons (240/(v+40)) and their one-hour delay, resulting in the inequality 240/v < 240/(v+40) + 1.

Step-by-step explanation:

The question asks for an inequality that models the situation where the Jacksons and the Simpsons are competing in a race, with the Jacksons starting an hour before the Simpsons. Assuming the Jacksons' average speed is v kilometers per hour, we can set up the time taken for both the Jacksons and the Simpsons to complete the 240-kilometer race.

For the Jacksons, the time taken to complete the race would be 240/v hours. The Simpsons, starting an hour later at a speed of v + 40 km/h, would have the time taken as 240/(v+40) hours plus the 1 hour delay. For the Jacksons to win, their time must be less than the time the Simpsons took. Therefore, the inequality in terms of v would be:

240/v < 240/(v+40) + 1