Question

Gil is now 80 miles ahead of Larry. Gil is traveling at a constant rate. Larry is traveling in the same direction, at a rate 5 miles per hour faster than Gil. In how many hours will Larry catch up to Gil?

A. 16
B. 15
C. 12
D. Larry cannot catch up to Gil.

Answer 1

It will take Larry 16 hours to catch up to Gil.

Step-by-step explanation:

To determine in how many hours Larry will catch up to Gil, we need to find the time it takes for Larry to cover the 80-mile distance between them. Since Larry is traveling at a 5 miles per hour faster rate than Gil, we can set up a equation:

Distance = Rate × Time

Let's assume that Larry catches up to Gil after t hours. Gil's rate is r miles per hour, and Larry's rate is r + 5 miles per hour. The equation becomes:

80 = (r+5)t

Since Gil is now 80 miles ahead of Larry, we can also write an equation for Gil's distance using Gil's rate:

(Gil's distance) = (Gil's rate) × t

80 = rt

Now we can set up a system of equations:

80 = (r + 5)t

80 = rt

Simplifying the equations gives:

rt + 5t = 80

rt = 80

Substituting rt = 80 in the first equation gives:

80 + 5t = 80

5t = 80

t = 16

Therefore, it will take Larry 16 hours to catch up to Gil. The correct option is A. 16.