Two buses leave a city at the same time,one going north and the other east.The north bound bus travels 10km/hr faster than the east bound one.If they are 250km apart after 5hours,What is the speed of each bus?

Answer 1

If one going north and the other east distance will be:

√ { ( 5 x )² + [ 5 ( x + 10 ) ]² } = 250

5 ( x + 10 ) = 5 x + 50

So:

√ [ ( 5 x )² + ( 5 x + 50 )² ] = 250

√ [ 25 x ² + 25 x² + 500 x + 50² ] = 250

√ ( 50 x² + 500 x + 2 500 ) = 250

50 x² + 500 x + 2 500 = 250²

50 x² + 500 x + 2 500 = 62 500

50 x² + 500 x + 2 500 - 62 500 = 0

50 x² + 500 x - 60 000 = 0

The solutions are:

x = - 40 an x = 30

Speed can't be negative, so speed of slower bus:

x = 30 km / h

speed of faster bus = x + 10 = 30 + 10 = 40 km / h

After 5 hrs, the slower went 30 ∙ 5 = 150 km

the faster went 40 ∙ 5 = 200 km

√ [ ( 150)² + ( 200)² ] = √ ( 22 500 + 40 000) = √ 62 500 = 250 km