A freight train left Washington and traveled south.

Question

A freight train left Washington and

traveled south. A diesel train left six hours

later traveling at 85 km/h in an effort to

catch up to the freight train. After

traveling for 11 hours the diesel train

finally caught up. What was the freight

train's average speed?

Answer 1

Hi Dylan,

To solve this problem we can treat the speed of the trains, the distance traveled, and the time elapsed as variables:

F = Speed of the freight train

D = speed of the diesel train

X = distanced traveled by the freight train

Y = distance traveled by the diesel train

t = time since the diesel train left the station

To find the distance the trains had gone at any time we would need to multiply their speed by the time elapsed, giving us the equations:

Y = D*t

X = F*( t +6 )

(we use t + 6 here because the freight train left the station 6 hours before the diesel train)

Because we know that the trains have travelled the same distance at 11 hours we know the following is true:

t = 11

Y=D

Because Y and D are equal we now know that:

F*(t+6) = D*t

By substituting 11 for t we get:

F*(11+6) = D*11

We already know the speed of the Diesel train is 85 km/hour so we can substitute that in for D, giving us:

F*(11+6) = 85*11

Simplify to get:

F*17 = 935

Divide both sides by 17 and and we find our answer:

F = 55

So the speed of the freight train is 55 km/hour

Answer 2

the flight train traveled x km/hr for 17 hours

diesel tran traveled 85km/hr for 11 hrs

17x=11(85+x)

17x=935+11x

6x=935

x=155.83 km/h