Question

A man travels uphill to city c from city b in a car at the speed of 40 km/hr, and returns to city b at a faster speed of 60 km/hr. what is his average speed for the round trip

Answer 1

Let the Distance travelled by man = x km

Speed (S1) = 40 km/h

Speed (S2)= 60 km/h

Time taken by man to travel from city B to C(T1)= Distance/ speed(s1)

T1= x/40= x/40 h

Time taken by man to return from city C to B(T2)= Distance/ speed(s2)

T2= x/60

Total time taken (T) = T1+T2

T= x/40+x/60=( 3x+2x)/120= 5x/120

T= x/24 h

Total distance (D)= x+x= 2x

Average speed= Total Distance (D)/Total time (T)

Average speed = D/T= 2x / (x/24)

= 2x×( 24/x)= 48 km/h

Hence, His average speed for the round trip= 48 km/hr

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Hope this will help you....

Answer 2

Given :

Let us assume that distance travelled by man is x m.

Speed of Man from city b to c is =v1=40km/hr

Speed of Man from city c to b is=v2=60 km/hr

Let  t1 be the time taken by man to reach from distance b to c :

t1=Distance/speed

  = x/40

⇒t1=x/40 hr

Let  t2  be the time taken by man to reach from distance c to b :

t2=Distance/speed
  = x/60
⇒t2=x/60 hr

Total time =t=  t1+t2

                 = x/40 + x/60
By taking L.C.M

= x/40 + x/60

=3x+2x/120

=5x/120
 =x/24 hr

∴Total time = t= X/24 hr

Total distance =x+x=2x

Now let us calculate the average speed:

Formula to be used : Average speed = Total speed/ Total Time
                                         
 Average speed  =2x/x/24
⇒48km/hr

∴ The average speed for the round trip is 48 km/hr