cardriven 850mile,has gone 5 miles per hour faster, made the trip in 2 hour less what was the speed?

Answer 1

distance = rate * time

850 = (r)(t) // original speed
850 = (r + 5)(t - 2) // faster speed

The first equation solves as t = 850/r, which we can substitute into the second one:

850 = (r + 5)(t - 2)
850 = (r + 5)(850/r - 2)
850 = 850 - 2r + 4250/r - 10
2r + 10 - 4250/r = 0
2r^2 + 10r - 4250 = 0
r^2 + 5r - 2125 = 0

r = (-5 +/- sqrt(5^2 - 4*1*-2125))/2
r = (-5 +/- sqrt(8525))/2
r = (-5 +/- 92.331 ) / 2

r = 43.666, r = -48.666

Ignoring the negative solution, r = 43.666 mph

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Checking the answer:

At original rate, t = 850/43.666 = 19.466 hours

At faster rate, t = 850/48.666 = 17.466 hours

Difference is two hours, to three significant digits.

Answer 2

850/v - 850/(v+5) = 2
850*(5) / (v^2 + 5v) = 2
v^2 + 5v - 425*5 = 0
2v = -5 +/- sqrt[5*5 + 4*5*425]
= -5 +/- sqrt[25*341]
v = 43.665 mph