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

Answer:

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

Step-by-step 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

Answer 2

Answer:

$\frac{2xz + 3xy}{5yz} \: seconds$

solution,

$time = \frac{distance}{speed}$

Let race be X meters.

Total time taken:

$\frac{40 \: percent \: of \: x}{y \: metre\: per \: second} + \frac{60 \: percent \: of \: x}{z \: metre \: per \: second} \\ = \frac{40}{100} \times \frac{x}{y} + \frac{60}{100} \times \frac{x}{z} \\ = \frac{2}{5} \times \frac{x}{y} + \frac{3}{5} \times \frac{x}{z} \\ = \frac{1}{5} ( \frac{2x}{y} + \frac{3x}{z} ) \\ = \frac{x}{5} ( \frac{2z + 3y}{yz} ) \\ = \frac{2xz + 3xy}{5yz} \: seconds$

hope this helps...

Good luck on your assignment...