AboutAbe Mantell Expertise Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience Over 15 years teaching at the college level.
Question The Gateway Arch in St.Louis is 640 ft high. How long would it take an object to fall freely from the top?
Sandi's Subaru travels 280 mi at a certain speed. If the car had gone 5 mph faster, the trip would have taken 1 hr less. Find Sandi's speed.
Answer 1. Using s(t)=(1/2)gt^2, with s(t)=640 ft and g=32 ft/sec^2, we get
. 640=16t^2 ==> t^2=40 ==> t=sqrt(40) or about 6.32 seconds
2. let x=the speed of the car, and t=the time to drive 280 miles.
.. Thus, xt=280...with (x+5)(t-1)=280, i.e. 5 mph faster & 1 hr less time
.. the first equation gives t=280/x, now substitute that into the 2nd
.. equation ==> (x+5)(280/x-1)=280, multiplying by x gives:
.. (x+5)(280-x)=280x ==> 280x+1400-x^2-5x=280x ==> x^2+5x-1400=0
.. which factors: (x+40(x-35)=0...so x=-40 or +35
Taking the positive result, Sandi's speed was 35 mph.
