Aja and pete are biking on a trail.
aja begins 2 miles ahead of pete and bikes at an average speed of 3 miles per hour.
pete bikes at an average speed of 4 miles per hour.

how much time will it take for pete to catch up with aja on the trail?

2 hours

Step-by-step explanation:

Given in the question that,

speed of Aja = 3 miles/h

speed of Pete  = 4 miles/h

we know that Aja is 2 miles away from Pete  

Both will have covered same distance at the time they will catch up.

suppose time = x

               distance covered = y

Formula to use

distance = speed x time

Equation 1

3x  = y - 2

3x + 2 = y

Equation 2

4x = y

Equate both equation

3x + 2 = 4x

2 = 4x -3x

2 = x

Pete will catch up Aja after 2 hours

Step-by-step explanation:

We can represent thsi problem as as system of equations.

Let

x =  be the time in which both Aja and Pete starte biking, (in hours)

y = the number of miles traveled by each

Aja begins 2 miles ahead of Pete and bikes at an average speed of 3 miles per hour. This means

y_Aja =  3*x + 2

Pete bikes at an average speed of 4 miles per hour.

y_Pete =  4*x

Then, we can find the intersection point between the graphs, so we find the solution.

Please see attached picture below

Pete will catch up Aja after 2 hours