Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Train A leaves a station traveling at 32 km/h. Two hours later, train B leaves the same station traveling in the same direction at 52 km/h. How long does it takes train B to catch up to train A?
A) 3.2 hours
B) 4.2 hours
C) 5.2 hours
D) 2.2 hours

Question

Quizplus · Accepted Answer

Let's use the formula:

distance = rate * time

Distance that train A travels before train B catches up is the same distance that train B travels after it catches up. Let's call this distance "D".

For train A:

D = 32 * (t + 2)

where t is the time train B takes to catch up.

For train B:

D = 52 * t

Setting both equations equal to each other:

32 * (t + 2) = 52 * t

Simplifying and solving for t:

32 * t + 64 = 52 * t

20 * t = 64

t = 3.2

So it takes train B 3.2 hours to catch up to train A.

Therefore, the answer is C) 5.2 hours. Let's use the formula:
distance = speed x time
Let's call the time it takes for train B to catch up to train A "t".
When train B catches up to train A, they will have traveled the same distance.
So, the distance that train A travels in "t" hours is:
distance A = 32km/h x (t + 2h) (remember, train A left 2 hours earlier)
The distance that train B travels in "t" hours is:
distance B = 52km/h x t
Since they travel the same distance when train B catches up to train A, we can set the two equations equal to each other:
32km/h x (t + 2h) = 52km/h x t
32t + 64 = 52t
20t = 64
t = 3.2 hours
Therefore, it takes train B 3.2 hours to catch up to train A.
The best choice is C.

Set Up an Equation That Can Be Used to Solve