Please help and read the description

Question

Wendy took a trip from one city to another, a distance of 510 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 30 mi/h, and the train averaged 95 mi/h. The entire trip took 10 1/2h. How long did Wendy spend on the train?

Answer 1

Not sure why this was classified as quadratic equations is it is a system of linear equations.  I am unaware of any quadratic setup that would help you.

 

Let x = number of hours traveled by bus.  Therefore the bus distance would be 30x since it is going 30 mi/h.

Let y = number of hours traveled by train.  Therefore the train distance would be 95x since it is going 95 mi/h.

 

Total time: x + y = 10.5

Total distance: 30x + 95y = 510

 

Solving the first equation for y: y = 10.5 - x

Substitute into the second equation:  30x + 95(10.5 - x) = 510.

Solve:

 

30x + 997.5 - 95x = 510

-65x + 997.5 = 510

-65x = -487.5

x = 7.5

 

Wendy rode the bus for 7.5 hours and the train for 10.5-7.5 or 3 hours.