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

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

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

then $\displaystyle x = 50km/h$

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 $\displaystyle x'=50+15=65km/h$

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

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