I live outside of town and commute to Chicago. I leave my house by 15 minutes af

Question

I live outside of town and commute to Chicago. I leave my house by 15 minutes after 8 and get onto I-90 at Exit 52. I must exit I-90 at Exit 12 by no later than 8:50 so that I am not late for class. Normally, I can drive the speed limit and make it on time.

Over the past few years there has been a lot of construction on Interstate 90. For example, last year 4 miles of road was under construction between Mile Marker 26 and 30. The posted speed limit in the construction zone (single lane -- do not pass) is 55 mph, but I always end up behind someone that is going only 52mph. When I am not in the Construction Zone, what is the minimum speed that I have to drive, so that I can be at Exit 12 by 8:50?

Explanation / Answer

Total distance = 40 miles

Total time = 35 min

Average speed = 40/35 miles/min = 40*60/35 miles/hr

According to question:

40/(4/52 + 36/x) = 40*60/35

1/13 + 36/x = 35/60

36/x = 0.506

x = 71.01 miles / hour

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