Question

Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan’s train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be?

The time when the two trains reach each other is
.

The trains are
away from the city when they reach each other.

Answer 1

question one is B and question 2 is C

Explanation:

Answer 2

1.25 hours.

68.75 miles from the city

Explanation:

Eltan's train (E) is travelling 65mph west.

Dmitri's train (D) is travelling 55mph west.

In terms of vectors, we can write E as 65E and D as 55W

The miles travelled by each is a function of time, T, in hours.

Each train's distance is:

E: T*65E

D: T*55W

They are 150 miles apart. They will meet with the combined miles travelled is 150 miles.

150 miles = T*65E + T*55W

150 miles = T(120 miles/hour)

T = (150 miles/120 miles/hour)

T = 1.25 hours

Make Demitri's train mile 0 and Eitan's train at mile 150 at the start.

They will have travelled the following miles in 1.25 hours:

Demitri: (1.25hr)(55 m/hr) = 68.75 miles

Eitan: (1.25hr)(65 m/hr) = 81.25 miles

Total = 150 miles

Dimitri is headed away from the city. After 1.25 hours, his train will have travelled 68.75 miles when he sees Eitan passing him on the adjacent track (hopefull) headed into the city. They meet 68.75 miles from the city.