Speed, Time & Distance — Case Study Based Questions

Two stations X and Y are 760 km apart. Two trains A and B start at the same time from X and Y respectively and move towards each other. It is known that A takes 5 hours to travel 620 km, while B covers 810 km in 4.5 hours.

1. The speed of the train A in km/hr is :
   (a) 124
   (b) 120
   (c) 132
   (d) 125

2. The speed of the train B in km/hr is :
   (a) 124
   (b) 136
   (c) 160
   (d) 180

3. The distance of the point where the two trains meet, from station X, is :
   (a) 450 km
   (b) 360 km
   (c) 310 km
   (d) 380 km

4. The time after which the two trains meet, is :
   (a) 3 hrs
   (b) 2 hrs 30 min.
   (c) 2 hrs 36 min.
   (d) 2 hrs 40 min.

Answer

1. Given,

Distance covered by train A = 620 km and time taken = 5 hours

By formula,

$\text{Speed of train A} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{620 \text{ km}}{5 \text{ hrs}}\\[1em] = 124 \text{ km/hr }$

Hence, option (a) is the correct option.

2. Given,

Distance covered by train B = 810 km and time taken = 4.5 hours

By formula,

$\text{Speed of train B} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{810 \text{ km}}{4.5 \text{ hrs}}\\[1em] = 180 \text{ km/hr }$

Hence, option (d) is the correct option.

3. As the two trains move towards each other,

Relative speed = 124 km/hr + 180 km/hr = 304 km/hr

$\text{Time taken to meet} = \dfrac{\text{Distance between X and Y}}{\text{Relative speed}}\\[1em] = \dfrac{760 \text{ km}}{304 \text{ km/hr}}\\[1em] = \dfrac{5}{2} \text{ hrs } = 2.5 \text{ hrs }$

Distance of the meeting point from station X = Distance covered by train A in 2.5 hrs

= 124 × 2.5 km = 310 km

Hence, option (c) is the correct option.

4. As the two trains move towards each other,

Relative speed = 124 km/hr + 180 km/hr = 304 km/hr

$\text{Time taken to meet} = \dfrac{760 \text{ km}}{304 \text{ km/hr}}\\[1em] = \dfrac{5}{2} \text{ hrs }\\[1em] = 2\dfrac{1}{2} \text{ hrs }\\[1em] = 2 \text{ hrs } 30 \text{ min}$

Hence, option (b) is the correct option.

Rajan is travelling from his home to a town 240 km away. For the first quarter of the journey, he takes a bus that travels 100 km in 2.5 hours. For the remaining journey, he takes a cab that covers 252 km in 3.5 hours.

1. The speed of the bus in km/hr is :
   (a) 36
   (b) 40
   (c) 32
   (d) 48

2. The speed of the cab in km/hr is :
   (a) 72
   (b) 64
   (c) 56
   (d) 75

3. The total time taken by Rajan to reach his destination is :
   (a) $3\dfrac{1}{2}$ hrs.
   (b) 4 hrs.
   (c) $4\dfrac{1}{2}$ hrs.
   (d) 5 hrs.

4. The average speed of Rajan for the complete journey in km/hr is :
   (a) 54
   (b) 56
   (c) 60
   (d) 48

Answer

1. Given,

Distance covered by the bus = 100 km and time taken = 2.5 hours

By formula,

$\text{Speed of the bus} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{100 \text{ km}}{2.5 \text{ hrs}}\\[1em] = 40 \text{ km/hr }$

Hence, option (b) is the correct option.

2. Given,

Distance covered by the cab = 252 km and time taken = 3.5 hours

By formula,

$\text{Speed of the cab} = \dfrac{\text{Distance}}{\text{Time}} = \dfrac{252 \text{ km}}{3.5 \text{ hrs}}\\[1em] = 72 \text{ km/hr }$

Hence, option (a) is the correct option.

3. Distance covered by bus = first quarter of the journey = $\dfrac{240}{4}$ km = 60 km

$\text{Time taken by bus} = \dfrac{60 \text{ km}}{40 \text{ km/hr}} = \dfrac{3}{2} \text{ hrs }\\[1em] = 1.5 \text{ hrs }$

Distance covered by cab = 240 km − 60 km = 180 km

$\text{Time taken by cab} = \dfrac{180 \text{ km}}{72 \text{ km/hr}} = \dfrac{5}{2} \text{ hrs }\\[1em] = 2.5 \text{ hrs }$

Total time taken = 1.5 hrs + 2.5 hrs = 4 hrs

Hence, option (b) is the correct option.

4. Total distance covered = 240 km

Total time taken = 4 hrs

By formula,

$\text{Average speed} = \dfrac{\text{Total distance covered}}{\text{Total time taken}}\\[1em] = \dfrac{240 \text{ km}}{4 \text{ hrs}}\\[1em] = 60 \text{ km/hr }$

Hence, option (c) is the correct option.