If the speed were increased by 10mph a 420 mile trip wud tak

If the speed were increased by 10mph, a 420 mile trip wud take and hour less. how long will the trip take at the slower speed?

Solution

Original:
rate = x
time = t
distance = xt = 420 ~> x = 420/t
Increased:
rate = x + 10
time = t - 1
distance = (x + 10)(t - 1) = 420
Plug:
(x + 10)(t - 1) = 420
(420/t + 10)(t - 1) = 420
420 + 10t - 420/t - 10 = 420
10t - 420/t = 10
10t^2 - 10t - 420 = 0
10t^2 - 70t + 60t - 420 = 0
(10t^2 - 70t) + (60t - 420) = 0
10t(t - 7) + 60(t - 7) = 0
(10t + 60)(t - 7) = 0
t = -6 or t = 7 .. no negative time values ... t = 7 hours