Question

a man drove his car for 20kms at an average speed of 25kms per hour.if his average speed for the whole distance of 40kms is to be 30kms per hour,then for the next 20kms his average speed will be options are (a)37kms/hour,(b)37*1/2kms/hour,(c)38kms/hour and (d)38*1/2kms/hour

Answer 1

Question:

A man drove his car for 20km at an average speed of 25km/hr. If his average speed for the whole distance of 40km is to be 30km/hr, then for the next 20km his average speed will be :

(a) 37km/hr

(b) 37½ km/hr

(c) 38 km/hr

(d)38½ km/hr

Answer:

(b) 37½ km/hr

Note:

Speed = Distance/time

Average speed = Total distance / total time taken.

Solution:

∆. For the first 20km journey, we have ;

Distance, AC = 20 km

Speed, V1 = 25 km/hr

Time = T1 hr

Now,

We know that,

=> Speed = Distance/Time

=> V1 = AC/T1

=> 25 = 20/T1

=> T1 = 20/25

=> T1 = 4/5

∆. For the next 20km journey, we have ;

Distance, CB = 20 km

Speed = V2 km/hr

Time = T2 hr

Now,

We know that,

=> Speed = Distance/Time

=> V2 = CB/T2

=> V2 = 20/T2

=> T2 = 20/V2

∆ . For the whole 40km journey, we have ;

Distance, AB = 40 km

Speed, V = 30 km/hr

Time = T

Now,

We know that,

=> Speed = Distance/Time

=> V = AB/T

=> 30 = 40/T

=> T = 40/30

=> T = 4/3

Also,

Time taken to cover AB = Time taken to cover AC

+ Time taken to cover CB

=> T = T1 + T2

=> 4/3 = 4/5 + 20/V2

=> 20/V2 = 4/3 - 4/5

=> 20/V2 = (4•5 - 4•3)/3•5

=> 20/V2 = (20 - 12)/15

=> 20/V2 = 8/15

=> V2 = 20•15/8

=> V2 = 75/2

=> V2 = 37½

Hence,

The required speed to cover next 20 km must be 37½ km/hr.