When a man travels equal distance at speed x km/h and y km/h, his average speed is 4 km/h. But when he travels at these speed for equal time, his average speed is 4.5 km/h. The difference of the two speed is ?
Answers
Answer:
average speed is 4.5 km per hour
Step-by-step explanation:
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.
Answer:
Suppose the equal distance = D km
Then, time taken with x and y speed are x
D h and
y
D h, respectively,
Case I:
Average speed Total time
Total distance =
4
x
D
y
D
2D =
+ x y
2xy & 4 + = ...(1)
Case II:
Average speed x y
2 = + = 4 5. km/h
x y + = 9 ...(2)
On putting this value in Eq. (1), we get,
xy
9
2 = 4 & xy = 18 ...(3)
Now, difference between two speed = x y -
Now, x y 2 ^ h - x y xy 4 2 = ^ h + - 9 4 18 2 = ^ ^ h h -
(From Eq. (2) and (3)]
= 81 72 -
x y 2 ^ h - = 9 & x y - = 3 ...(4)
On adding Eq. (2) and (4), we get
2x = 12
x 2
12 = = 6
On putting the value of x in Eq. (4), we get
6 - y = 3
y = 3
Hence, x = 6 km/h and y = 3 km/h
and, their difference = 633 - = km/h.