A man jogs at a speed of 1.1 m/s. his dog waits 1.6 s and then takes off running at a speed of 2.4 m/s to catch the man. how far will they have each traveled when the dog catches up with the man?

To solve this problem, let us first assign variables.

Let us say that,

A = man

B = dog

And the distance travelled by man and dog must be equal, therefore:

dA = dB

From the linear equations, we know that the formula for distance d is:

d = v t

where v is velocity and t is time, therefore:

vA tA = vB tB

We are given tA = tB + 1.6 s, therefore:

vA (tB + 1.6) = vB tB

1.1 (tB + 1.6) = 2.4 tB

1.1 tB + 1.76 = 2.4 tB

1.3 tB = 1.76

tB = 1.354 s

Therefore they both travelled a distance of:

dA = dB = 1.354 s * 2.4 m/s = d

d = 3.25 m