# Time and Distance

Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h

$$\frac{S_{1}}{S_{2}} = \sqrt{\frac{t_{2}}{t_{1}}}$$

⇒ $$\frac{120}{S_{2}} = \sqrt{\frac{9}{16}} = \frac{3}{4}$$

⇒ $$S_{2} = 160$$ km/h

How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

Speed = 9 km/hr

= $$\left(9 \times \frac{5}{18} \right )$$ m/sec

= $$\frac{5}{2}$$ m/sec

Distance = (35 × 4) m = 140 m.

Time taken = $$\left(140 \times \frac{2}{5} \right )$$ sec

= 56 sec

A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

Number of gaps between 41 poles = 40

So total distance between 41 poles = 40 × 50

= 2000 meter = 2 km

In 1 minute train is moving 2 km/minute.

Speed in hour = 2 × 60 = 120 km/hour

Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, $$\frac{5}{6}$$ hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?

If the speed of the faster horse be $$f_{s}$$ and that of slower horse be $$s_{s}$$ then

$$f_{s} + s_{s} = \frac{50}{1} = 50$$

and $$\frac{50}{s_{s}} - \frac{50}{s_{s}} = \frac{5}{6}$$

Now, you can go through options.

The speed of slower  horse is 20 km/h

Since,   20 + 30 = 50

and $$\frac{50}{20} - \frac{50}{30} = \frac{5}{6}$$

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

Similarly, anticlockwise she has four different routes.

Total routes = 8

A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is

Time taken in walking both ways = 7 hours 45 minutes --------(i)

Time taken in walking one way and riding back= 6 hours 15 minutes -------(ii)

By equation (ii) × 2 − (i), we have

Time taken to man ride both ways, = 12 hours 30 minutes − 7 hours 45 minutes

= 4 hours 45 minutes

A train covers a distance in 50 minutes, if it runs at a speed of 48 kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.

Lets solve it.

Time = $$\frac{50}{60}$$ hr = $$\frac{5}{6}$$ hr

Speed = 48 mph

Distance = S × T = $$48 \times \frac{5}{6}$$ = 40 km

New time will be 40 minutes so,

Time = $$\frac{40}{60}$$ hr = $$\frac{2}{3}$$ hr

Now we know,

Speed = Distance/Time

New speed = 40 \times \frac{3}{2} kmph = 60kmph

Two boys starting from the same place walk at a rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?

In this type of questions we need to get the relative speed between them,

The relative speed of the boys = 5.5 kmph – 5 kmph
= 0.5 kmph

Distance between them is 8.5 km

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

$$Time = \frac{8.5 \: km}{0.5 \: kmph}$$ = 17 hrs

The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?

Substitute sensible numbers and work out the problem. Then change the numbers back to letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put $$\frac{6}{2}$$ caps on per minute, or $$\left ( \frac{6}{2} \times 60 \right )$$ caps per hour. Putting letters back this is 60 c/m. If you divide the required number of caps (b) by the caps per hour you will get time taken in hours. This gives bm/60c