Larry's time to travel 364 miles is 3 hours more than Terrell's time to travel 220 miles. Terrell drove 3 miles per hour faster than Larry. How fast did each one travel?

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Answer 1 · 2015-11-12T14:54:32

Terrell's speed #= 55# mph
Larry's speed #= 52# mph

Let #x# be Larry's travel time.

#=>#Terrell's travel time #= x - 3#

Let #y# be Larry's speed

#=>#Terrell's speed #= y + 3#

#xy = 364#

#=> x = 364/y#

#(x - 3)(y + 3) = 220#

#=> (364/y - 3)(y + 3) = 220#

#=> ((364 - 3y)/y)(y + 3) = 220#

#=> (364 - 3y)(y + 3) = 220y#

#=> 364y + 1092 - 3y^2 - 9y = 220y#

#=> -3y^2+ 355y + 1092 - 220y = 0#

#=> -3y^2 + 135y + 1092 = 0#

#=> y^2 - 45y + 364 = 0#

#=> (y - 52)(y + 3) = 0#

#=> y = 52, y = -3#

But since we are talking about speed, the value should be positive

#=> y = 52#

#=> y + 3 = 55#