SOLUTION: two families who lived 63 miles apart met at a park between their homes for a picnic. how long did each drive if both travelled at a rate of 45 miles an hour and one drove 12 minut

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Question 1065649: two families who lived 63 miles apart met at a park between their homes for a picnic. how long did each drive if both travelled at a rate of 45 miles an hour and one drove 12 minutes longer than the other? how to solve it?

Found 2 solutions by rothauserc, josmiceli:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
use rate * time = distance
:
r(1) * t(1) + r(2) * t(2) = 63
:
12 minutes = 12 / 60 = 1 / 5 = 0.2 hour
:
we are given r(1) = r(2) = 45, t(1) = t + 0.2 and t(2) = t
:
45(t + 0.2) + 45t = 63
:
45t + 9 + 45t = 63
:
90t = 54
:
t = 54 / 90 = 6 / 10 = 0.6
:
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family one drove 0.8 hour or 48 minutes
:
family two drove 0.6 hour or 36 minutes
***************************************
:

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = the distance in miles that the
one who drove for the shorter time traveled
= the distance in miles the one
who drove for the longer time traveled
Let = time in hrs that the one who
drove for the shorter time traveled
= time in hrs that the one
who drove for the longer time traveled
----------------------------------------
(1)
(2)
----------------------------------
( note that )
(2)
(2)
Substitute (1) into (2)
(2)
(2)
(2) hrs
Convert to minutes
(2)
(2) min
and

----------------------
One drove for 36 min
The other drove for 48 min
---------------------------
check:
(1) ( must be in hrs here )
(1)
(1) mi
and
(2)
(2)
(2)
(2)
(2)
(2) mi
OK