# Time and Distance

A car is running at a speed of 108 kmph. What distance will it cover in 15 second?

Speed = 108 kmph = $$\left ( 108 \times \frac{5}{18} \right )$$ m/sec = 30 m/sec

∴ Distance covered in 15 sec. = (30 × 15) m = 450 m

A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minutes. The ratio of their speeds is :

Ration of speed = $$\left ( \frac{550}{60} \times \frac{18}{5} \right ) : \left ( \frac{33}{45} \times 60 \right )$$

= 33 : 44

= 3 : 4

An athlete runs 200 metres race in 24 seconds.His speed is :

Speed = $$\frac{200}{24}$$ m/sec

= $$\frac{25}{3}$$ m/sec

= $$\left ( \frac{25}{3} \times \frac{18}{5} \right )$$ km/hr

= 30 km/hr

Which of the following trains is the fastest ?

25 m/sec = $$\left ( 25 \times \frac{18}{6} \right )$$ km/hr = 90 km/hr.

And, 25 m /sec = (25 × 60) m/min = 1500 m/min.

So, all the three speeds  are equal.

A person crosses a 600 m long street in 5 minutes.What is his speed in km per hour?

$$Speed = \left ( \frac{600}{5 \times 60} \right )$$ m/sec

= 2 m/sec

= $$\left ( 2 \times \frac{18}{5} \right )$$ km/hr

= 7.2 km/hr.

A person crosses a 600 m long street in 5 minutes.What is his speed in km per hour?

$$Speed = \left ( \frac{600}{5 \times 60} \right )$$ m/sec

= 2 m/sec

= $$\left ( 2 \times \frac{18}{5} \right )$$ km/hr

= 7.2 km/hr.

A train passes a 50 metres long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of the train is:

Let the length of train be L m.

$$\frac{L}{10} = \frac{L + 50}{14}$$

14L = 10L + 500

L = 125 m.

$$Speed = \left ( \frac{25}{2} \right )$$ m/s

= $$\left ( \frac{25}{2} \right ) \times \frac{18}{5}$$

= 45 km/hr

A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds. The length of the train (in metres) is:

Let the length of train be L m.

Acc. to question

$$\frac{264+L}{20} = \frac{L}{8}$$

2112 + 8L = 20L

$$L = \frac{2112}{12}$$ = 176 m

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Let the length of the train be L m.

$$\frac{L}{8} = \frac{264+L}{20}$$

20L = 8L + 2112

L = 176 m.

Speed of train = $$\frac{176}{8}$$ = 22 m/s = $$22 \times \frac{18}{5}$$ = 79.2 km/hr

A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds in passing him. The speed of the train was

Let the train’s length be L m.

$$\frac{L}{9} = \frac{L + 84}{21}$$

21L = 9L +756

12L = 756

L = 63 m

$$\frac{63}{9}$$ =7 m/s = $$7 \times \frac{18}{5}$$

Speed = $$\frac{63}{9}$$ =7 m/s = $$7 \times \frac{18}{5}$$ = 25.2 Km/hr.