Answer:
The speed/rate to her parent's house is x = 75 mph
The speed/rate from her parent's house is y = 50 mph
Explanation:
Given;
Distance to her parent's house = 240 miles
Total distance travelled (to and fro) = 240×2 = 480 miles
Total time taken t = 8 hours
On her way there her average speed was 25 miles per hour faster than on her way home (she ran into some bad weather)
Let x and y represent her speed to and from her parent's house respectively.
x = y+25 ......1
The time taken to her parent's house is;
time = distance/velocity
t1 = 240/x = 240/(y+25)
The time taken from her parent's house is;
time = distance/velocity
t2 = 240/y
Total time taken t = t1 +t2
t = 240/(y+25) + 240/y = 8
Solving for y ;
(240y + 240(y+25))/(y^2 +25y) = 8
Cross multiply;
240y + 240y+6000 = 8y^2 + 200y
480y +6000 = 8y^2 + 200y
8y^2 + 200y -480y -6000 = 0
8y^2 - 280y - 6000 = 0
Divide through by 8;
y^2 - 35y - 750 = 0
Solving the quadratic equation;
y = 50
or
y = -15
Velocity cannot be negative, so y = 50mph
From equation 1;
x = y+25
Substituting y =50
x = 50 + 25
x = 75 mph
The speed/rate to her parent's house is x = 75 mph
The speed/rate from her parent's house is y = 50 mph