Question

Rafael boards a train to Michigan. The train is 1.5 miles long and runs at a speed of 10 miles per hour. If the train crosses the station in 30 minutes, find the station's length.

• A. 3.5 miles
• B. 7.5 miles
• C. 4 miles
• D. 2.5 miles

Answer 1

The correct option is A 3.5 miles

Length of train = 1.5 miles
Speed of train = 10 miles per hour
Time taken to cross the station = 30 minutes

30 minutes:
$=\frac{30}{60}\text{hour}$

$=\frac{1}{2}\text{hour}$

= 0.5 h

We know,
$Speed=\frac{Distance}{Time}$

Here,
$Speedoftrain=$

$\frac{Lengthoftrain+Lengthofstation}{Timetakentocrossthestation}$

Let the length of the station be S miles.

Thus,
$10=\frac{1.5+S}{0.5}$

$\Rightarrow 10\times 0.5=1.5+S$

⇒ 5 – 1.5 = S

⇒ 3.5 = S

Thus, the station is 3.5 miles long.