When a man travels equal distance at equal distance at speeds of V1 and V2 km/hr ,his average speed is 4 km/hr. But, when he travels at these speeds for equal time his average speed is 4.5 km/ hr.Find the difference between 2 speeds.
Answers
Answer:
3km/h
Step-by-step explanation:
Case I :
Let the total distance be 2d.
Time = Distance / Speed
Total time :
d/V1 + d/V2 = 2d/4
Divide through by d to get :
1/V1 + 1/V2 = 2/4
1/V1 + 1/V2 = 1/2
Case II
Distance = Time × Speed
Let the total time be 2t.
Total distance will be :
t × V1 + t × V2 = 2t × 4.5
Divide through by t to get :
V1 + V2 = 9
From this we can get :
V1 = 9 - V2
We substitute this in case 1 to get :
1/(9 - V2) + 1/V2 = 1/2
Eliminating the denominators we have :
V2 × 2 + 2(9 - V2) = (9 - V2)V2
Let V2 = x
2x + 18 - 2x = 9x - x²
18 = 9x - x²
This forms a quadratic equation :
x² - 9x + 18 = 0
The roots are - 3 and - 6
Expanding we have :
x² - 3x - 6x + 18 = 0
x(x - 3) - 6(x - 3) = 0
(x - 6)(x - 3) = 0
x = 3 or 6
The value of V2 = 3 or 6
If we take 3 then :
1/3 + 1/V1 = 1/2
2V1 + 6 = 3V1
3V1 - 2V1 = 6
V1 = 6
The two speeds are :
6km/h and 3km/h
The difference is :
6 - 3 = 3 km/h
Answer:
Answer:
3km/h
Step-by-step explanation:
Case I :
Let the total distance be 2d.
Time = Distance / Speed
Total time :
d/V1 + d/V2 = 2d/4
Divide through by d to get :
1/V1 + 1/V2 = 2/4
1/V1 + 1/V2 = 1/2
Case II
Distance = Time × Speed
Let the total time be 2t.
Total distance will be :
t × V1 + t × V2 = 2t × 4.5
Divide through by t to get :
V1 + V2 = 9
From this we can get :
V1 = 9 - V2
We substitute this in case 1 to get :
1/(9 - V2) + 1/V2 = 1/2
Eliminating the denominators we have :
V2 × 2 + 2(9 - V2) = (9 - V2)V2
Let V2 = x
2x + 18 - 2x = 9x - x²
18 = 9x - x²
This forms a quadratic equation :
x² - 9x + 18 = 0
The roots are - 3 and - 6
Expanding we have :
x² - 3x - 6x + 18 = 0
x(x - 3) - 6(x - 3) = 0
(x - 6)(x - 3) = 0
x = 3 or 6
The value of V2 = 3 or 6
If we take 3 then :
1/3 + 1/V1 = 1/2
2V1 + 6 = 3V1
3V1 - 2V1 = 6
V1 = 6
The two speeds are :
6km/h and 3km/h
The difference is :
6 - 3 = 3 km/hr