Question

Hazel needs to get to her granddaughter's house by taking an airplane and a rental car. She travels 900 miles by plane and 250 miles by car. The plane travels 250 mph faster than the car. If she drives the rental car for 2 hours more than she rode the plane, find the speed of the car.

Answer 1

50 pmh

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:

`900= (c + 250)((250)/(c) -2)\\\\ 900=250 +(62500)/(c)-2c-500\\\\ 1150=(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`

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