Question

At 10a.m. Juan leaves the city traveling north at 60 mi/hr. One hour later mel leaves the city traveling south at 50 mi/hr. At what time will they be 830 miles apart?

Answer 1

$\frac{60}{1} = \frac{830}{x}$
$60x = 830$
$x = 13.83$
$10 + 13.83 = 23.83$
23.83 hours is around 11:50pm

$\frac{50}{1} = \frac{830}{x}$
$50x = 830$
$x = 16.6$
$11 + 16.6 = 27.6$
$27.6 - 24 = 3.6$
3.6 is around 1:36am

Answer 2

-- At 11 AM, when Mel starts out, Juan has already covered 60 miles.

-- After that, since they're traveling in opposite directions, the distance
between them increases (60 + 50) = 110 miles every hour.

Let's call 'H' the number of hours after 11 AM.
Then the distance between them is

D = 110H + 60

When is this distance 830 miles ?  Wouldn't you like to know !

830 = 110H + 60

Subtract 60 from each side:

770 = 110H

Divide each side by 110 :

H = 770 / 110 = 7 .

It happens 7 hours after 11 AM.
That would be 6:00 PM .