Tatiana left the coffee shop traveling 8 mph. Then, 3 hours later, Laura left traveling the same direction at 20 mph. How long until Laura catches up with Tatiana?

T distance = 8 t

L distance = 20 (t-3)
so
8 t = 20 t - 60
60 = 12 t
t = 5
t-3 = 2 hours for Laura

To determine how long it takes for Laura to catch up with Tatiana, we need to find the time it takes for them to be at the same position.

Let's first calculate the distance Tatiana covers in the 3 hours before Laura starts.

Distance = Speed × Time
Distance = 8 mph × 3 hours
Distance = 24 miles

Now that we know Tatiana has traveled 24 miles before Laura starts, we can use the relative speed between Laura and Tatiana to find out how long it will take for Laura to catch up.

Relative Speed = Laura's Speed - Tatiana's Speed
Relative Speed = 20 mph - 8 mph
Relative Speed = 12 mph

The relative speed of 12 mph means that Laura is closing the distance with Tatiana by 12 miles every hour.

To find the time it takes for Laura to catch up, we divide the initial distance between them (24 miles) by the relative speed.

Time = Distance / Relative Speed
Time = 24 miles / 12 mph
Time = 2 hours

Therefore, it will take Laura 2 hours to catch up with Tatiana.