Answer:
50 pmh
Step-by-step explanation:
Distance traveled by plane = 900 miles
Distance traveled by car = 250 miles
Let the speed of the car is c. The plane travels 250 mph faster than the car, so speed of the plane will be c + 250
Let the time taken to travel on car is t. She traveled 2 hours more on car the she rode on plane. This means she consumed 2 hours less time on plane. So the time spent on plane will be t - 2 hours.
Distance = Speed x Time
For Plane, the equation will be:
900 = (c + 250)(t - 2) Equation 1
Likewise, the equation for car will be:
250 = ct
From here, t = 250/c
Using this value in Equation 1, we get:
[tex]900= (c + 250)(\frac{250}{c} -2)\\\\ 900=250 +\frac{62500}{c}-2c-500\\\\ 1150=\frac{62500}{c}-2c\\\\ 1150c=62500-2c^{2}\\\\ 2c^{2}+1150c-62500=0\\\\ \text{Using the quadratic formula, we get}\\\\ c=\frac{-1150\pm \sqrt{1150^{2}-4(2)(-62500)} }{2(2)}\\\\ c = -625, 50[/tex]
Since value of speed cannot be negative, we only consider the positive value. So from here we can conclude that the speed of the car was 50 mph
