To find out how long it will be until Helen and Elizabeth meet, we first need to calculate their combined speed.
Helen's speed is 95 kilometers per hour, and Elizabeth's speed is 89 kilometers per hour.
The combined speed is:
\[ 95 , \text{km/h} + 89 , \text{km/h} = 184 , \text{km/h} \]
Next, we need to determine how long it takes for them to cover the total distance between them, which is 77 kilometers. We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting in the values we have:
\[ \text{Time} = \frac{77 , \text{km}}{184 , \text{km/h}} \]
Calculating this gives:
\[ \text{Time} = 0.4184 , \text{hours} \]
To convert this time into minutes, we multiply by 60:
\[ 0.4184 , \text{hours} \times 60 , \text{minutes/hour} = 25.104 , \text{minutes} \]
Rounding to the nearest minute, we get:
\[ \text{Time} \approx 25 , \text{minutes} \]
Thus, it will be approximately 25 minutes until Helen and Elizabeth meet.