Question

Sam and Naomi are having a race. Sam runs 5 yards for every 3 yards Naomi runs. Sam gives Naomi a 20 yard head start. How many yards does Sam have to run to catch up with Naomi?

Answer 1

Answer:

Sam has to run 50 yards to catch up with Naomi.

Solution:

Given that Sam and Naomi are having a race.

Sam runs 5 yards for every 3 yards Naomi runs.  

This means that when Naomi runs $3 \times x$ that is 3x yards, Sam runs $5 \times x$ that is 5x yards.

Also Sam gives Naomi a 20 yard head start

Let say Sam catch up Naomi at point A.

Let say Naomi run 3x yard to reach point A. So Sam ran 5x yards to reach point A.

Distance need to covered by Sam = distance covered by Naomi + 20 yard head start

=>5x = 3x + 20

=>5x – 3x = 20

=> 2x = 20

=> x = 10

Number of yards covered by Sam to reach catching point A = 5x = 5 $\times$ 10 = 50 yards

Hence Sam have to run 50 yards to catch up with Naomi.