Question

In a 100m race, the ratio of Zena's time to Yvonne's Time is 4:5. if zena hd taken 2 seconds more and yvonne had taken 1 second less, the ratio would be 1:1. find zena's time.

Answer 1

To find Zena's time in the 100m race given a ratio and conditions, we can set up and solve a system of equations. Zena's time is found to be 8 seconds.

Step-by-step explanation:

To find Zena's time in the 100m race, we can set up a proportion using the given ratios. Let Z represent Zena's time and Y represent Yvonne's time:

Z/Y = 4/5

Since we know that if Zena took 2 seconds more and Yvonne took 1 second less, the ratio would be 1:1, we can set up another proportion:

(Z+2)/(Y-1) = 1/1

Solving these two proportions simultaneously, we can find Zena's time.

First, we cross multiply the first proportion:

5Z = 4Y

Then, we cross multiply the second proportion:

Z+2 = Y-1

Next, we can substitute 4Y for 5Z in the second equation:

Z + 2 = 4Y - 4

Simplifying the equation:

3Y - Z = 6

Now we have a system of equations:

5Z = 4Y

3Y - Z = 6

Solving this system of equations, we find that Z = 8 seconds. Therefore, Zena's time in the 100m race is 8 seconds.

Answer 2

By setting up equations based on the given ratios and solving for the variables, we can determine that Zena's original time for the 100m race is 12 seconds.

Step-by-step explanation:

The student is asking about finding Zena's time for a 100m race given a ratio of times between Zena and Yvonne and a hypothetical scenario that alters this ratio.

The original ratio of Zena's time to Yvonne's time is given as 4:5. We can set up two equations based on the information provided:

1. Let Z represent Zena's original time, and Y represent Yvonne's original time. We have Z/Y = 4/5.
2. If Zena had taken 2 seconds more and Yvonne had taken 1 second less, the ratio of their times would be 1:1. So, (Z + 2)/(Y - 1) = 1/1, which simplifies to Z + 2 = Y - 1.

From equation 1, we can write Z = 4Y/5. Substituting this into equation 2 gives us 4Y/5 + 2 = Y - 1.

Multiplying both sides of the equation by 5 to clear the fraction, we get 4Y + 10 = 5Y - 5.

Now, solving for Y, we get Y = 15 seconds for Yvonne's time.

Substituting Y back into the first equation, Z = 4Y/5, we find Z = 4(15)/5, which gives us Z = 12 seconds for Zena's time.