Question

A passenger train leaves the train station 5 hours after a freight train left the same station. The freight train is traveling 30 mph slower than the passenger train. Which equation helps to find the rate of each train, if the passenger train overtakes the freight train in three hours.

A. 3r = 5(r - 30)


B. 3r = 8(r + 30)

C. 5r = 3(r - 30)


D. 3r = 8(r - 30)

Answer 1

3r = 8(r-30), D

Explanation:

so lets look at how the rates correlate to each other first

passenger train is 30 mph faster, so

r - 30 = r1,

where r1 is the freight train

and r is the passenger train

so in order to find the position of the trains, you multiply the rate by time

for example, to find the distance of the freight train, it would be

8(r1), as it has been traveling for 8 hours when they intersect

so that would be the same as 8(r-30)

the positions should equal when they overtake eachother, so then for the passenger train, it has been traveling for only 3 hours, so itll be 3r

so 3r = 8(r-30)