Question

A train of length 0.7 miles crosses a bridge with a speed of 150 miles per hour in 30 seconds. Find the length of the bridge.

• A. 0.55 miles
• B. 1.20 miles
• C. 0.70 miles
• D. 0.60 miles

Answer 1

The correct option is A 0.55 miles

$\text{Speed}=\frac{Distance}{Time}$

Let the length of the bridge be x miles.

Speed of the train = 150 mph

Time taken = 30 seconds

$=\frac{30}{60\times 60}$ hours

Length of the train = 0.7 miles

Time taken by a train of length 'a' miles to pass a stationary object of length 'b' miles is the time taken to cover (a + b) miles.

Thus,

$\frac{0.7+x}{\frac{30}{60\times 60}}=150$

$\Rightarrow \frac{0.7+x}{30}\times 60\times 60=150$

$\Rightarrow (0.7+x)\times 120=150$

$\Rightarrow 0.7+x=\frac{150}{120}=1.25$

$\Rightarrow x=0.55$

Hence, the length of the bridge is 0.55 miles.