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# Help?? I don't get this?

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I drove to my parents' house at 60 miles per hour. If I had driven 50 miles an hour instead, then I would have gotten there 40 minutes later. How many miles did I drive?

Thank you!

Sep 18, 2018

#1
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The DISTANCE is the same regardless of the SPEED.

Let x = amount of hours required at 60 MPH

then x+ 40/60  = hours required at  50 MPH

Since the distance is equal:

60 * x  = 50 (x + 40/60)      Then slove for 'x' = 3 1/3 hr

60 mph  takes  3 1/3 hr   =  60 x 3 1/3  miles = 200 miles

Sep 18, 2018
#2
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Thank you!

Sep 18, 2018
#3
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Welclome!

Sep 18, 2018
#4
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Let D  be the distance...and 40 min  = 2/3 hr

And  rate * time  =  distance.....but the distances are the same...so  ...we can make an equation involving the times

Adding 40min  = 2/3 hr to  the time it takes driving 60 mph  = the time it takes driving 50  mph....so...

D / 60   +  2/3   =  D /  50    rearrange as

2/3=  D/50  - D / 60

2/3  = [ 60 - 50 ] D  / 3000

2/3  = 10D / 3000

2/3  = D/ 300    multiply both sides by 300

300 (2/3)  = D  = 200 miles

Sep 20, 2018