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?

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Answer 1 · 2018-04-23T02:32:04

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

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(t -1 ) quad # (valid for #t ge 1#)

They've met when

#30 t = 40(t - 1) = 40 t - 40#

#40 =10 t#

#t = 4 # hours

Check:

#30(4) = 120#

#40(4 - 1) = 120 quad sqrt #