Question 1122045
.
At 1 pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road. 
The bus overtook the motorist at 6 pm. The speed of the bus driver was 30 km per hour faster than the motorist.

Find the speed of the motorist.

Find the distance between X and Y if the bus was 60km from Y at 6pm.
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<pre>
The motorist spent 5 hours on the way from the start moment at 1 pm to catching moment at 6 pm.


The bus spent 2 hours less, i.e. only 3 hours from the start to the catching moment.


Both traveled the same distance, which gives you an equation


    5*x = 3*(x+30),


where x is the motorist speed (in kilometers per hour) and (x+30) is the bus speed.


Solve the equation 


    5x = 3x + 90


    3x - 3x = 90


    2x = 90  ====>  x = {{{90/2}}} = 45.


Thus the motorist speed is  45 km/k.  The bus speed is  45 + 30 = 75 km/h.


The bus traveled  3*75 = 225 kilometer.


The distance from X to Y  is  225 + 60 = 285 kilometers.


<U>Answer</U>.  The motorist speed was 45 kilometers per hour.


         The distance from X to Y  is  285 kilometers.
</pre>

Solved.


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