Eric ran from school to the town monument and back again. On his way to the monument, he ran at 10kph and went back to school at 8kph. The entire trip took 2 hours and 15 minutes. How far is the monument from school?

Distance = 10 km

Step-by-step explanation:

Let x be the number of hours taken from school to town and y be the number of hours taken back to the school

Then distance covered during first trip would be 10x (distance = speed*time) and during the second trip would be 8y. Both distances are equal.

=> 10x = 8y  

Dividing both sides by 2

=> 5x = 4y

=> 5x-4y = 0   (1)

The total time for both the trips is:

=> x + y = 2.25 (2)

Multiplying eq (2) by 5

=> 5x+5y = 11.25  (3)

Subtacting (3) from (1)

=> 5x-4y-5x-5y = 0-11.25

=> -4y-5y = -11.25

=> -9y = -11.25

Dividing both sides by -9

=> y = 1.25 hrs

Putting in (2)

=> x + 1.25 = 2.25

=> x = 2.25 - 1.25

=> x = 1 hr

Now, Calculating the Distance

=> Distance = 10x

=> 10 ( 1 )

=> Distance = 10 km

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step-by-step explanation: