At 8:00 a.m. the Smiths left a campground, driving at 48 mi/h. At 8:20 a.m. the Garcia's left the same campground and followed the same route, driving at 60 mi/h. At what time did they overtake the Smiths?

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Answer 1 · 2017-12-02T15:19:57

9:40 hours

Let Garcia will overtake Smith after x hour of her(Garcia) journey.

As Smith has started 20 minutes early (i.e. 8:20 - 8:00), so she has to travel (x + 20/60) hours.

In (x + 20/60) hours Smith goes = 48 * (x + 20/60) miles as she goes 48 miles per hour.

In x hours Garcia goes 60 * x = 60 x miles as she goes 60 miles per hour.
Now as per questions, #48 (x + 20/60) = 60 x#

#rArr 48 x + 48. 20/60 = 60 x #

#rArr 48 x + 16 = 60 x#

#rArr 48x - 60 x = -16#

#rArr -12 x = - 16 #

#rArr x = (-16)/(-12)#

#rArr x = 4/3 # = 1 hour 20 minutes.

Garcia will overtake Smith at 8:20 + 1:20 = 9:40 hours