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

Answer: (b)

\(\frac{S_{1}}{S_{2}} = \sqrt{\frac{t_{2}}{t_{1}}}\)

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

⇒ \(S_{2} = 160\) 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?

Answer: (d)

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?

Answer: (d)

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?

Answer: (d)

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?

Answer: (b)

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

Answer: (c)

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.

Answer: (b)

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?

Answer: (c)

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?

Answer: (a)

Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart.

Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11.

A machine puts c caps on bottles in m minutes. How many hours will it take to put caps on b bottles

Answer: (b)

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