Joe must travel 240 miles to attend a super-awesome Cardinal baseball game, and

Question

Joe must travel 240 miles to attend a super-awesome Cardinal baseball game, and Lauren must travel 300 miles to get there. Joe leaves 30 minutes after Lauren and drives a constant 65 mph for 2 hours, then speeds up to 72 mph for the remainder of the trip. Lauren hates to be late for first pitch, and certainly doesn't want Joe to beat her there. Knowing she must travel farther, she leaves 30 minutes before Joe and plans to drive a constant 74 mph. How long does it take Lauren to get to the game? How long does it take Joe to get to the game? Who arrives first?

Explanation / Answer

Lauren's time is pretty straight forward, she travels 300milesat 74 mph: 300miles * 1hr/74miles ˜ 4.05 hrs or 4 hrs3min Joe goes 65mph for the first 2 hrs, so he goes a total of 2*65= 130miles in the first 2 hours, then he has 240mi - 130mi = 110miles to go. During these last 110 miles he drives 72mph:100miles * 1hr/72miles ˜ 1.528 hrs or 1 hr 32min, so his totaltime is 2hrs + 1hr 32min = 3hrs 32 min Lauren left a half an hour before Joe so we can add half anhour to his time and then it's like he left at the same time, soJoe's new time is 3 hrs 32min + 30min = 4hrs 2min which is aminute less than Lauren's 4hrs 3min, so Joe arrives first

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