# 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?

## we have a chart for time multiplied by rate equals distance

Dec 2, 2017

9:40 hours

#### Explanation:

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, $48 \left(x + \frac{20}{60}\right) = 60 x$

$\Rightarrow 48 x + 48. \frac{20}{60} = 60 x$

$\Rightarrow 48 x + 16 = 60 x$

$\Rightarrow 48 x - 60 x = - 16$

$\Rightarrow - 12 x = - 16$

$\Rightarrow x = \frac{- 16}{- 12}$

$\Rightarrow x = \frac{4}{3}$ = 1 hour 20 minutes.

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