# Math Help - Rational Word Problem

1. ## Rational Word Problem

The average spped of an express train is 40km/h faster than the average speed of a bus. To travel 1200km, the bus requires 50% more time than the train. Determine the average speeds of the bus and the train.

Rough ideas

Train = 40 + x
Bus = x
Bus { 1200 = (1.5t)y
Train { 1200 = y

2. Hello, Quan!

We know this formula: . $\text{(Distance)} \:=\:\text{(Speed)} \times \text{}" alt="\text{(Distance)} \:=\:\text{(Speed)} \times \text{}" />

Since the problem compares the times of the two vehicles,

. . we will use this variation: . $\text{Time} \:=\:\frac{\text{Distance}}{\text{Speed}}$

The average spped of an express train is 40km/h faster than the average speed of a bus.
To travel 1200km, the bus requires 50% more time than the train.
Determine the average speeds of the bus and the train.

Let: $x$ = speed of bus.
Then: $x+40$ = speed of train.

The train's speed is $x+40$ km/hr.
. . To travel 1200 km, it takes: $\frac{1200}{x+40}$ hours.

The bus' speed is $x$ km/hr.
. . To travel 1200 km, it takes: $\frac{1200}{x}$ hours.

We are told that the bus' time is 50% more than the train's time.
. . That is, it is: $1\frac{1}{2} \:=\:\frac{3}{2}$ times the train's time.

There is our equation! . . . . . $\frac{1200}{x} \;=\;\frac{3}{2}\cdot\frac{1200}{x+40}$

Can you finish it now?