Question

After robbing a bank in dodge city, a robber gallops off at 14 mi/h. 20 minutes later, the marshall leaves to pursue the robber at 16 mi/h. how long (in hours) does it take the marshall to catch up to the robber?

Answer 1

For this case we have to write the equation of the position of each one.

We have then:

For the robber:

$r = 14t$

For the marshall :

$r = 16 (t- (\frac{20}{60}))$

$r = 16 (t-\frac{1}{3})$

By the time the marshall reaches the robber we have:

$14t = 16 (t-\frac{1}{3})$

From here, we clear the time.

We have then:

$16t - 14t = \frac{16}{3}$

$2t = \frac{16}{3}$

$t =\frac{8}{3}$

$t = 2.7 h$

Answer:

it takes the marshall to catch up to the robber about 2.7 hours.