Question

With summer winding down, Mr. and Mrs. Mallery decided to take their family to the beach one last time. They loaded their kids, Olivia and Liam, into the car and headed off early in the morning. At 7:05 Olivia asked, "Are we there yet?" "We're one-third of the way there," replied Mr. Mallery. = At 7:25 Liam asked, "Are we there yet?" "We're 75% of the way there," said Mrs. Mallery. "Now, can you two figure out what time we should get to the beach?" Assuming the Mallerys maintain a constant speed during their trip, at what time they will arrive at the beach? 7:05​

Answer 1

They will arrive at the beach at 8:05 AM.

Let's break this down step by step.

At 7:05, Mr. Mallery says they are one-third (1/3) of the way there.

At 7:25, Mrs. Mallery says they are 75% of the way there, which is 3/4.

The difference between these two updates is the distance they traveled in 20 minutes (from 7:05 to 7:25).

They went from 1/3 to 3/4 of the way in 20 minutes, which means they covered another 2/3 of the remaining distance in that time (3/4 - 1/3 = 2/3).

Since this 2/3 of the distance was covered in 20 minutes, we can figure out how long it would take to cover the whole distance:

1 (total distance) = 2/3 (covered in 20 minutes) * (60 minutes / 20 minutes)

1 = 2/3 * 3

1 = 2

So, they will take 60 minutes to cover the whole distance at their constant speed.

Now, let's calculate the time:

They started at 7:05 and will take 60 minutes to reach the beach, so:

7:05 + 1 hour = 8:05

They will arrive at the beach at 8:05 AM.