Answer:
Time Spent = 91.46 minutes
Step-by-step explanation:
Given
To Her Father's house
Distance = 164 miles
Time Taken = 2 hours
To Her Cousin's house
Distance = 125 miles
Required
Time Taken to get to her cousins house.
First, her average speed to her father's house needs to be calculated.
Speed is calculated as thus;
[tex]Speed = \frac{Distance}{Time}[/tex]
In this case, Distance = 164 miles and Time = 2 hours
Substitute these values;
[tex]Speed = \frac{164 miles}{2 hours}[/tex]
[tex]Speed = 82miles/hour[/tex]
It's stated in the question that; she maintains the same speed when going to her cousin's residence to spend the night;
Using the same formula for speed;
[tex]Speed = \frac{Distance}{Time}[/tex]
But in this case, Speed = 82 miles/hour and Distance = 125 miles
Substitute these values
[tex]82 = \frac{125}{Time}[/tex]
Multiply both sides by Time
[tex]82 * Time = \frac{125}{Time} * Time[/tex]
[tex]82 * Time = 125[/tex]
Divide both sides by 82
[tex]\frac{82 * Time}{82} = \frac{125}{82}[/tex]
[tex]Time = \frac{125}{82} hours[/tex]
To convert this time to minutes
If 1 hour = 60 minutes
Then,
[tex]\frac{125}{82} hours[/tex] is equivalent to [tex]\frac{125}{82} * 60 minutes[/tex]
Hence,
[tex]Time = \frac{125}{82} * 60 minutes[/tex]
[tex]Time = 91.463415 minutes[/tex]
[tex]Time = 91.46 minutes[/tex] (Approximated)
Hence, she spends 91.46 minutes to get to her cousin's place from her father's house
