Posted 21 Aug 2013 (edited) · Report post I drove x miles at 55 mph. I then drove x + 20 miles at 40 mph. I drove for a total of 100 minutes. How far did I drive? Edited 21 Aug 2013 by BMAD 0 Share this post Link to post Share on other sites

0 Posted 21 Aug 2013 · Report post 27 miles @55mph, then 47 miles@40 mph 0 Share this post Link to post Share on other sites

0 Posted 21 Aug 2013 · Report post t1 + t2 = 100 minutes = 100/60 hours t1 = x/55 t2 = (x+20)/40 x/55 + (x+20)/40 = 100/60 x = 1540/57 Total distance = x + (x+20) = 4220/57 miles = 74 2/57 miles 0 Share this post Link to post Share on other sites

0 Posted 21 Aug 2013 · Report post X = miles at 55 mph X+20 = miles driven at 40 mph and 55 mi/ hr = 0.917 mi/ min 40 mi/ hr = 0.667 mi/ min D = Total Distance = D1 (at 55 mph) + D2 (at 40 mph) T = Total Time = T1 (at 55 mph) + D2 (at 40 mph) D1 = T1 ( 0.917 mi/ min) D2 = T2 ( 0.667 mi/ min) Therefore D = D1 + D2 = T1 ( 0.917 mi/ min) + T2 ( 0.667 mi/ min) We also know that D1 +20 = D2 These can be rearranged into 2 simultaneous equations in the form 20 0 Share this post Link to post Share on other sites

0 Posted 21 Aug 2013 · Report post X = miles at 55 mph X+20 = miles driven at 40 mph and 55 mi/ hr = 0.917 mi/ min 40 mi/ hr = 0.667 mi/ min D = Total Distance = D1 (at 55 mph) + D2 (at 40 mph) T = Total Time = T1 (at 55 mph) + D2 (at 40 mph) D1 = T1 ( 0.917 mi/ min) D2 = T2 ( 0.667 mi/ min) Therefore D = D1 + D2 = T1 ( 0.917 mi/ min) + T2 ( 0.667 mi/ min) We also know that D1 +20 = D2 These can be rearranged into 2 simultaneous equations in the form 20 I hit the wrong key 20 = - T1 ( 0.917 mi/ min) + T2 ( 0.667 mi/ min) [Eqn 1] 100 = T1 +T2 [Eqn 2] Multiplying all terms in Eqn 1 by {- 1/0.667} yeilds -30 = 1.375 T1 - T2 Adding this to Eqn2 results in 70 = 2.375 T1 Therefore T1 = 70 /2.375 = 29.47 min, so D1 = 29.47 min * ( 0.917 mi/ min) = 27.02 D2 = D1 + 20 = 47.02 Therefore Total distance = 74.04 Miles 0 Share this post Link to post Share on other sites

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I drove x miles at 55 mph. I then drove x + 20 miles at 40 mph. I drove for a total of 100 minutes. How far did I drive?

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