How far is it from Central City to Clear Creek?

Question

It takes a passenger train 2 hours less that it takes a freight train to make the trip from Central City to Clear Creek. The passenger train averages 96km/h while the freight train averages 64 km/h. How far is it from Central City to Clear Creek?

Answer 1

S1 = speed of the passenger = 96km/h

t1 = time it took the passenger 

t2 = time it took the freight

S2 = speed of the freight = 64km/h

"It takes a passenger train 2 hours less that it takes a freight train" means t1 = t2 -2

Distance = S1 * t1 = s2 * t2

s1 * (t2 -2) = s2 * t2

96(t2-2)=64*t2

96t2 - 192 = 64t2

t2=6hours

Distance = 64*6 = 348km

I hope this helps

Answer 2

Let's call x the distance between the two cities.

 

If the freight train averages 64 km/h, then the time it takes the freight train should be x / 64.  That's because distance / speed = time.

 

Similarly, the time it takes the passenger train should be x / 96.

 

Since the passenger train takes 2 hours less than the freight train, you can write this out as an equation:

 

x / 96 = x / 64 - 2.

 

To solve this, first add 2 to both sides:

x / 96 + 2  = x / 64

 

Get the x's on the same side by subtracting x / 96 from both sides:

2 = x / 64 - x / 96

 

Combine the fractions.  The least common denominator is 192:

2 = 3x / 192 - 2x / 192

2 = x / 192

 

Multiply both sides by 192:

384 = x

 

So the distance is 384 km.