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# The Rooney family drives to Pittsburg at 60 mph and returns by a road 10 miles shorter...

schooledmom | Salutatorian

Posted June 20, 2013 at 1:54 PM via web

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The Rooney family drives to Pittsburg at 60 mph and returns by a road 10 miles shorter at 65 mph. The return trip takes 30 minutes less.  How long is each road?

Tagged with algebra 1, math

llltkl | College Teacher | Valedictorian

Posted June 20, 2013 at 2:16 PM (Answer #1)

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Let the road-distance from Rooney family’s house to Pittsburg, travelled by them in the forward journey be ‘d’ miles. So, the road-distance travelled in their return journey was (d-10) miles.

Time taken in the forward journey = distance / speed = d/60 hrs.

Time taken in the return journey = distance / speed = (d-10)/65 hrs.

By condition of the problem, difference between these two times is 30 minutes= 30/60 hrs. = 1/2 hrs.

Hence,

`d/60-(d-10)/65 = 1/2`

`rArr (13d-12d+120)/780 = 1/2` (LCM of 60 and 65 is 780)

`rArr (d+120)/780 = 1/2`

cross multiplying,

`2d = (780-240)=540`

`rArr d= 540/2 = 270` .

Therefore,  the distance of the road travelled by the Rooney  family’s house to Pittsburg was 270 miles, and the distance of the road travelled by them in the return journey was (270-10) = 260 miles.

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