This question is about Quadratic Equations and Algebra

Question

A train travels at an average speed from Quadratic City to Trinomial Town, a distance of 63 km. Then, without

stopping, it travels a distance of 72 km to Factoring County at an average speed that’s 6km/h faster than its original

speed. If it takes a total of 3 hours to complete the full journey from Quadratic City to Factoring County, what was

the train’s original speed? Solve algebraically.

Answer 1

63/s +72/(s+6)= 3

multiply by LCD

63(s+6) +72s = (s+6)3s

63s + 378 +72s = 3s^2 +18s

combine like terms

3s^2 -117s -378 = 0

divide by 3

s^2 - 39s -126 = 0

factor if possible

or use the quadratic formula

(s-42)(s+3) = 0

s = 42 mph = original speed

check the answer replace s with 42 in the original equation

63/42 + 72/48 = 21/14 + 24/16 = 3/2 + 3/2 = 3 It works