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Question

A freight train requires 2.5 hours longer to make a 300-mile journey than an express train does. If the express train averages 20 miles per hour faster than the freight train, how long does it take the express train to make the trip?

Answer 1

distance = rate of speed times time traveled

d=rt

300 = F(2.5+T) = 2.5F + FT = E(T)= (20+F)T = 20T + FT

where F= speed of the freight train, E= speed of the express train. T = time for the express train to go 300 miles

20T + FT = 300

2.5F + FT = 300

20T - 2.5F = 0

4T - .5F = 0

F= 8T

20T + FT = 300

20T + 8T(T) = 300

8T^2 + 20T - 300 = 0

4T^2 + 10T -150 = 0

(4T+30)(T-5) = 0

T-5 = 0

T = 5 hours for the express train to go 300 miles

5 hours for the Express Train to go 300 miles at 60 mph

7.5 hours for the Freight Train to go 300 miles at 40 mph

5 x 60 = 300

7.5 x 40 = 300

7.5 = 5 + 25

60 = 40+ 20