Distance of two trains leaving at different times.

Question

A train left Miami and traveled toward NYC. 14 hours later a diesel train left traveling at 45km/hr in an effort to catch up to the train. After traveling for four hours the diesel train finally caught up. What was the train's average speed?

Answer 1

This is a d = rt problem, as you know.  Distance equals rate (speed) times time.

 

If you think about this problem, you will realize that the distance traveled by the two vehicles must be the same, since they start at the same point, and the problem ends when the diesel catches up.

 

Let r_t = the train's speed

Let t_t = t he train's time of travel

 

Likewise,

 

Let r_d = the diesel's speed

Let t_t = the diesel's time

 

Since d is the same for both,

 

r_tt_t = r_dt_d  (Transitive property, or two things equal to the same thing are equal to each other.)

 

Now substitute known values.  The diesel travels for 4 hours at 45 km/hr (given).  The train starts 14 hours earlier, so travels a total of 18 hours.  We now have three of the four variables evaluated and can solve for r_t.

 

r_t x 18 = 45 x 4

 

18 r_t = 180 (simplifying

 

r_t = 10  (dividing both sides by 18)

 

 

Answer 2

You need the distance formula for this. 

 

Let's let the train be d₁ and the diesel train be d₂. Then d₁=r₁t₁ and d₂=r₂t_2. Since the trains travel the same distance, we have

d₁=d₂

r₁t₁=r₂t₂. We want to find r₁.

 

r₁(18)=45(4). So r₁=10.