Question

Samantha is running a race that is x meters. She runs the first 40% of the race at y meters per second and the remainder of the race at z meters per second. How long, in seconds, does it take for Samantha to finish the race? A detailed explanation please :)

Answer 1

`(2xz + 3xy)/(5yz) \: seconds`

solution,

`time = (distance)/(speed)`

Let race be X meters.

Total time taken:

`(40 \: percent \: of \: x)/(y \: metre\: per \: second) + (60 \: percent \: of \: x)/(z \: metre \: per \: second) \\ = (40)/(100) * (x)/(y) + (60)/(100) * (x)/(z) \\ = (2)/(5) * (x)/(y) + (3)/(5) * (x)/(z) \\ = (1)/(5) ( (2x)/(y) + (3x)/(z) ) \\ = (x)/(5) ( (2z + 3y)/(yz) ) \\ = (2xz + 3xy)/(5yz) \: seconds`

hope this helps...

Good luck on your assignment...

Answer 2

t= 0.2x (2/y + 3/z)

Explanation:

Distance:

40% of the race= 0.4x

60% of the race= 0.6x

Speed:

y m/s at first part and z m/s at second part

Time:

time= distance/speed, it also consists on 2 parts due to different speed

t= 0.4x/y + 0.6x/z

or

t= 0.2x (2/y + 3/z) seconds is the answer