Question

Train A leaves the station traveling east at 55 mph, while train B leaves the station 45 minutes later traveling west at 70 mph. Choose the equation below that represents the distance in miles between the two trains, D, as a function of T, the time in hours after train B has departed.

A.
D = 125T
B.
D = 125T + 41.25
C.
D = 125T - 41.25
D.
D = 125T + 2475

Answer 1

Answer: b)
`D=125T+41.25`

Explanation:

Given,

speed of train A travelling east = 55 mph

speed of train B travelling west = 70 mph

time train A travelled while train B was at rest = 45 min or
`((3)/(4))hr`

so, Distance travelled by train A while train B was at rest =
`55((3)/(4) ) miles\\`

=
`41.25 miles`

Now, after 'T' hour both the train will travel;

train A = 55T

train B = 70T

hence, the distance (D) between two train in miles will be;

⇒ D = 41.25 + 55T + 70T

⇒ D = 125T + 41.25