A man covers a certain distance at the speed of x km/h and returns to the starting point at 56 km/h. If his average speed for the whole journey is 63 km/h, then what is the value of x?
- A75
- B72
- C80
- D70
Solution & Step-by-step Explanation
When a person travels equal distances at two different speeds, say v
1
and v
2
, the average speed for the entire journey is given by the harmonic mean formula:
Average Speed=
v
1
+v
2
2⋅v
1
⋅v
2
Given:
Forward speed (v
1
) = x km/h
Return speed (v
2
) = 56 km/h
Average Speed = 63 km/h
Substituting these values into the formula:
63=
x+56
2⋅x⋅56
63(x+56)=112x
63x+3528=112x
112x−63x=3528
49x=3528
x=
49
3528
=72
1
and v
2
, the average speed for the entire journey is given by the harmonic mean formula:
Average Speed=
v
1
+v
2
2⋅v
1
⋅v
2
Given:
Forward speed (v
1
) = x km/h
Return speed (v
2
) = 56 km/h
Average Speed = 63 km/h
Substituting these values into the formula:
63=
x+56
2⋅x⋅56
63(x+56)=112x
63x+3528=112x
112x−63x=3528
49x=3528
x=
49
3528
=72