Two runners one averaging 5 miles per hour and the other one averaging 4 miles per hour, start at the same place and run along the same trail. the slower runner arrives at the end of the trail a half hour after the faster runner. how far did each person run?

The Distance cover by both the Runners is same = 10 miles  

Step-by-step explanation:

According to question ,

The Speed of first runners (S 1) = 5 miles per hour

The speed of second runners (S 2)  = 4 miles per hour

Let The Time taken by First runner (T 1 ) = T hour

But the second runner  arrives half hour after the first runner ,

I.e The Time taken by Second runner (T 2) = ( T + )

Now from Distance = Speed × Time

Since both the runners start from same place and run along the same trail

SO ,Both the Distance cover by both are same , D 1 = D 2

i.e Speed 1 × Time 1 = Speed 2 × Time 2

    5 mph × T            =  4 mph   ×  ( T + )

    5 T =  4 T + ( 4 × )

Or,  5 T - 4 T = 2

∴       T    =  2 hour  ,

Time take by first = T1 = T = 2 hour

Time take by second = T2 = T + = (2  +   )hour =

Now the Distance cover = Speed × Time

              Distance   (D1)          = 5 mph  × 2 hour = 10 mile

And        Distance    (D2)         =  4 mph  × = 10 miles

Hence, As The Distance cover by both the Runners is same = 10 miles  Answer

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