# A ship left a port and sailed east at the rate of 30 miles per hour. One hour later, a second ship left the same port at the rate of 40 miles per hour, also traveling east. In how many hours did the second ship overtake the first ship?

Apr 23, 2018

Four hours from the first ship leaving, or three hours from the second ship leaving.

#### Explanation:

Let $t$ be the elapsed time in hours, ${x}_{1}$ the distance ship 1 has traveled and ${x}_{2}$ the distance ship 2 has traveled..

${x}_{1} = 30 t$

${x}_{2} = 40 \left(t - 1\right) \quad$ (valid for $t \ge 1$)

They've met when

$30 t = 40 \left(t - 1\right) = 40 t - 40$

$40 = 10 t$

$t = 4$ hours

Check:

$30 \left(4\right) = 120$

40(4 - 1) = 120 quad sqrt