A train covered 1,200 mi at a certain speed. Had the train been able to travel 8 mph​ faster, the trip would have been 5 hr shorter. How fast did the train​ go?

Answer 1

rt = 1200, rate of speed times time = distance

(r+8)(t-5) = 1200

rt +8t -5r -40 = 1200

rt+ 8t-5r =1240

rt =1200

+8t-5r = 40

8t =5r+40

t =(5r+40)/8

rt = r(5r+40)/8) = 1200

5r^2/8 +5r = 1200

5r^2 -40r = 9600

r^2 +8r = 1920

(r+4)^2 = 1920+16 = 1936

r+4 = sqr1936=44

r = 44-4 = 40 mph = train's speed

t=(5r+40)/8 = (5(40)+40)/8 = 30 hours

rt=40(30) = 1200 miles

(r+8)(t-5) = 1200 miles

(48)(25) = 1200 miles