Question

Tom and Kimberly live 100 miles apart. Kimberly lives in a beautiful Spanish-style

home with a large pool. Tom lives in a penthouse apartment looking over the city.
They love each other's homes so much that they decided to switch homes!
Kimberly and Tom have packed all of their stuff and plan to make a total of five,
one-way trips to move everything from one home to the other. At the end of these
five, one-way trips, they will end up in their new homes.
X
They leave their respective homes at 7 am, Tom driving at an average of 65 mph
and Kimberly driving at an average of 60 mph. How many times (not when or where
will they cross paths if it takes them 20 minutes to load and/or unload at each
home? What time will they finish the move?

Answer 1

Answer:Since Tom and Kimberly are moving in opposite directions, they will cross paths at some point. Let's call the distance they will cover before they meet each other "x".

We can set up an equation to represent this:

x + (100 - x) = 100

Simplifying this equation, we get:

2x = 100 - x

Solving for x, we get:

x = 33.33 miles

This means that they will meet each other after traveling 33.33 miles from their respective homes. The time it takes to travel this distance can be calculated using the formula:

time = distance / speed

For Tom, the time taken to travel 33.33 miles at 65 mph is:

time = 33.33 / 65 = 0.5123 hours

Converting this to minutes, we get:

time = 0.5123 * 60 = 30.74 minutes

Similarly, for Kimberly, the time taken to travel 66.67 miles at 60 mph is:

time = 66.67 / 60 = 1.1111 hours

Converting this to minutes, we get:

time = 1.1111 * 60 = 66.67 minutes

Adding 20 minutes for loading and unloading at each home, the total time for each one-way trip is:

Tom: 30.74 + 20 + 20 = 70.74 minutes

Kimberly: 66.67 + 20 + 20 = 106.67 minutes

Since they are making five one-way trips, the total time for the move is:

Tom: 5 * 70.74 = 353.7 minutes

Kimberly: 5 * 106.67 = 533.35 minutes

To find out what time they will finish the move, we need to add the total time for the move to the time they started, which was 7 am. Let's convert the total time to hours:

Tom: 353.7 / 60 = 5.895 hours

Kimberly: 533.35 / 60 = 8.889 hours

Adding these times to 7 am, we get:

Tom: 7 am + 5.895 hours = 12:53 pm (rounded to the nearest minute)

Kimberly: 7 am + 8.889 hours = 3:53 pm (rounded to the nearest minute)

Therefore, they will finish the move at 12:53 pm and 3:53 pm, respectively.