Time and word problem

Question

Ben can run 70 yards in 15 seconds. Dylan can run the same distance in 18 seconds. If Dylan is 20 yards ahead of Ben when they both start running, how long does it take for Ben to catch Dylan?

Answer 1

70 yd/15s=4 2/3 yd/s

70yd/18s=3 8/9 yd/s

d=rt

x+20=(4 2/3)t

x=(3 8/9)t

(4 2/3)t-20=(3 8/9)t

(4 2/3)t-(3 8/9)t=20

(4 6/9)t-(3 8/9)t=20

(7/9)t=20

t=20(9/7)

t=180/7

t=25.714 seconds

Answer 2

Assume the velocity of both Ben and Dylan are the same at any time in both scenarios.

Then the average velocity is the same as velocity at any point.

v1 = Ben's Average Velocity = 70 yards/15 seconds = 4.67 yards/sec

v2 = Dylan's Average Velocity = 70 yards/18 seconds = 3.89 yards/sec

 

The equation for displacement in one dimension kinematics is

x(t) = x0 + vt + at²

 

From our initial assumption, a = 0 because velocity doesn't change.

Let x1 be Ben's displacement and x2 be Dylan's displacement

 

x1 = 4.67t

x2 = 20 + 3.89t

 

We must find the point where x1 = x2

20 + 3.89t = 4.67t

0.78t = 20

t = 25.64 seconds