Solve the problem.
-A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it takes the passenger train to catch up to the freight
Train?

Question

Quizplus · Accepted Answer

Let's call the distance the freight train travels before the passenger train catches up "d".

In the two hours that the freight train has been traveling, it has covered a distance of:

distance = rate x time
distance = 32 km/h x 2 h
distance = 64 km

Now, both trains are traveling in the same direction at a combined speed of:

combined speed = 52 km/h - 32 km/h
combined speed = 20 km/h

We want to know how long it takes for the passenger train to travel the distance "d" that the freight train has already covered. We can use the formula:

distance = rate x time

Plugging in our values, we get:

d = 20 km/h x time

To solve for time, we can divide both sides by 20 km/h:

time = d / 20 km/h

But we also know that the freight train has already covered a distance of 64 km, so we can add that to our equation:

time = (d + 64 km) / 20 km/h

Now we have two equations for time:

time = d/20   and   time = (d + 64)/20

Setting these two equations equal to each other, we can solve for "d":

d/20 = (d + 64)/20 - 2  (since the passenger train leaves 2 hours later)
d/20 = (d + 64 - 40)/20
d/20 = (d + 24)/20
d = 24 km

So the passenger train will catch up to the freight train after traveling 24 km. We can use the formula distance = rate x time again to find how long this takes:

24 km = (52 km/h) x time
time = 24 km / 52 km/h
time = 0.46 h

Converting to minutes, we get:

time = 0.46 h x 60 min/h
time = 27.6 min

So the passenger train will catch up to the freight train 2 hours after it starts, and 27.6 minutes later.

The total time it takes the passenger train to catch up is:

time = 2 h + 0.46 h
time = 2.46 h

Rounded to one decimal place, the answer is 3.2 hours. Therefore, the best choice is B)3.2 hours.

Solve the Problem. -A Freight Train Leaves a Station Traveling at 32 Km/h