Question

The length of time, in hours, it takes a train to travel to City B varies inversely with the train's speed. The train Carole is traveling on is moving at a speed of 70 miles per hour, and it takes her 4 hours to arrive. If the train that Steve is traveling on is moving at a speed of 50 mph, how long will it take him to arrive at City B?

87.55 hours

2.6 hours

5.6 hours

280 hours

Answer 1

To solve this problem, we start with the principle of inverse variation. According to the problem, the time \( t \) it takes to travel to City B varies inversely with the speed \( s \) of the train. This can be expressed mathematically as:

\[
t \times s = k
\]

where \( k \) is a constant.

From Carole's journey:
- Speed \( s_C = 70 \) mph
- Time \( t_C = 4 \) hours

We can calculate the constant \( k \):

\[
k = t_C \times s_C = 4 \times 70 = 280
\]

Now, for Steve's journey, we have:
- Speed \( s_S = 50 \) mph

We want to find the time \( t_S \):

\[
t_S \times s_S = k
\]

Plugging in the values we have:

\[
t_S \times 50 = 280
\]

Now we can solve for \( t_S \):

\[
t_S = \frac{280}{50} = 5.6 \text{ hours}
\]

Thus, the time it will take Steve to arrive at City B is **5.6 hours**.

The correct answer is: **5.6 hours**.