Question

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?

Answer 1

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

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 +
`(1)/(2)` )

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 +
`(1)/(2)` )

5 T = 4 T + ( 4 ×
`(1)/(2)` )

Or, 5 T - 4 T = 2

∴ T = 2 hour ,

Time take by first = T1 = T = 2 hour

Time take by second = T2 = T +
`(1)/(2)` = (2 +
`(1)/(2)` )hour =
`(5)/(2)`

Now the Distance cover = Speed × Time

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

And Distance (D2) = 4 mph ×
`(5)/(2)` = 10 miles

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