I need help answering this using Quadratic Equations. Please, also explain in detail what you did, so I KNOW how to do it for next time.

The time required for a train to make a 175 km trip is 1.5 hours less than the time required by bus. The average speed of the bus is 15 km/hr less than that of the train for the same trip. Find the average speed of the train.

Thanks =)

2. hi
let $x$ $km/h$ be the speed of the bus.
$\left(x-15 \right)\left(\frac{175}{x}+1.5 \right) = 175$

$\frac{3\,{x}^{2}+305\,x-5250}{2\,x} = 175$

$\frac{3\,{x}^{2}-45\,x-5250}{2\,x} = 0$

then $x = 50km/h$

and we know that the average speed of the bus is 15 km/hr less than that of the train, hence the average speed of the train is $x'=50+15=65km/h$

3. thank you ^^
but the answer key which i have been given from my teacher, says that the speed of the train is just 50km/hr.

:s

4. well,i think $50 km/h$ is the speed of the bus,but i might be wrong,let me check.

5. sorry about later i was wrong
let $x$ be the speed of the train and $y$ the speed of the bus,we have :
$x = y + 15$
and
$\left(y+15 \right)\left(\frac{175}{y}-1.5 \right)=175$
$-\frac{3\,{y}^{2}+45\,y-5250}{2\,y} = 0$
then $y = 35$ $km/h$
hence $x = 50$ $km/h$