Question

Alberto ran a race at a speed of 9 meters per second. Omar had a 6 meter head start and ran at a speed of 7 meters per second. Both started running at the same time. How many seconds did it take Alberto to catch up to Omar and how far had Alberto run?

Answer 1

Answer: Alberto run 27 meters.

Time taken By Alberto=3 seconds

Step-by-step explanation:

Let d be the distance Alberto ran to catch Omar.

Then, distance ran by Omar=x-6

Also, $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

Since, both started running at the same time.

Time taken By Alberto=$\frac{x}{9}$

Time taken By Omar=$\frac{x-6}{7}$

Now, at the point they meet time taken by both is equal.

$\frac{x}{9}=\frac{x-6}{7}\\\Rightarrow\ 7x=9(x-6)\\\Rightarrow7x=9x-54\\\Rightarrow9x-7x=54\\\Rightarrow\ 2x=54\\\Rightarrow\ x=27$

Hence, Alberto run 27 meters.

Time taken By Alberto=$\frac{27}{9}$=3 seconds