# Problem solving

• Aug 8th 2006, 09:11 PM
xXxSANJIxXx
Problem solving
A tourist bus leaves Townsville and heads North. It travels at an average speed of 50 km/h. It does not stop until it reaches the small and little known settlement of Goanna Creek. A second tourist bus leaves Townsville 2 hours later than the first and travels at an average speed of 70 km/h. The second bus arrives at Goanna Creek at the same time as the first bus. How far is Goanna Creek from Townsville? :D
• Aug 8th 2006, 10:07 PM
CaptainBlack
Quote:

Originally Posted by xXxSANJIxXx
A tourist bus leaves Townsville and heads North. It travels at an average speed of 50 km/h. It does not stop until it reaches the small and little known settlement of Goanna Creek. A second tourist bus leaves Townsville 2 hours later than the first and travels at an average speed of 70 km/h. The second bus arrives at Goanna Creek at the same time as the first bus. How far is Goanna Creek from Townsville? :D

Let the distance be $d$, then the first bus takes $t=d/50 \mbox{ hr}$,
and the second bus takes $t-2=d/70 \mbox{ hr}$.

Hence substituting from the first of these into the second gives:

$d/50-2=d/70 \mbox{ hr}$,

which you need to solve to find the distance.

RonL
• Aug 9th 2006, 03:00 AM
xXxSANJIxXx
thanx
• Aug 9th 2006, 08:07 AM
Soroban
Hello, xXxSANJIxXx!

The Captain had the best solution . . . direct and simple.

Here's a baby-talk approach.
(It's not as efficient, but it has worked for me many times.)

Quote:

A tourist bus leaves Townsville and heads North at an average speed of 50 kph.
It does not stop until it reaches the small and little known settlement of Goanna Creek.
A second tourist bus leaves Townsville 2 hours later than the first and travels at 70 kph.
The second bus arrives at Goanna Creek at the same time as the first bus.
How far is Goanna Creek from Townsville?

Bus $A$ had a two-hour headstart . . . it has already gone 100 km.
Code:

          : - - 100 - - : - - - 50t - - - : Bus A    T-------------+-----------------G Bus B    T-------------------------------G           : - - - - -  70t  - - - - - - - :

During the next $t$ hours, bus A travels $50t$ km and reaches Goanna Creek.

During the same $t$ hours, bus B travels $70t$ km, the entire distance.

Since their distances are equal: . $70t\:=\:50t + 100\quad\Rightarrow\quad t = 5$ hours.

So bus B drove for 5 hours at 70 kph . . . the distance is: $\boxed{350\text{ km}}$