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

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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