SOLUTION: 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 little known settlement of Goanna Creek. A s

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Question 42056: 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 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?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the distance between Townsville and Goanna Creek = x km.

For first bus:
Distance to be traveled = x km.
Average speed = 50 km/h.
Therefore, time taken = DISTANCE%2FSPEED = x%2F50 hours.

For second bus:
Distance to be traveled = x km.
Average speed = 70 km/h.
Therefore, time taken = DISTANCE%2FSPEED = x%2F70 hours.

The second bus started 2 hrs. after the departure of the first bus but both reached the destination at the same time.
So, the second bus takes 2 hr. less time than the first bus to complete the journey.

So we can write,
(Time taken by second bus in hrs.) = (Time taken by first bus in hrs.) - 2
or x%2F70+=+x%2F50+-+2
or x%2F50+-+x%2F70+=+2
or %2870x-50x%29%2F%2850%2A70%29+=+2
or 20x%2F%2870%2A50%29+=+2
or x%2F%287%2A50%29+=+1
or x = 350

Hence, the reqd. distance is 350 km.