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1

Ilya and Anya each can run at a speed of 8.30mph and walk at a speed of 3.90mph . They set off together on a route of length 5.00miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.

How long does it take Anya to cover the distance of 5.00miles ?

Express your answer numerically, in minutes.

Find Anya's average speed.

Express Anya's average speed save,Anya numerically, in miles per hour.

How long does it take Ilya to cover the distance?

Express the time tIlya taken by Ilya numerically, in minutes.

Now find Ilya's average speed.

Express Ilya's average speed save,Ilya numerically, in miles per hour.

Edit
Added Tue, 29 Mar '16
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Solutions
2

Given , Running speed(RS) = 8.3 mph

Walking Speed (WS) = 3.9 mph

Total distance = 5 miles

Time taken by Anya to cover the distance = (2.5/3.9) +(2.5/8.3) hours

= [ (2.5/3.9) + (2.5/8.3) ] * 60 mins

= 56.53 minutes

Anya's average speed = (5/56.53)*60 mph = 5.30 mph

Time taken by Ilya to cover the distance =

let time taken by Ilya to cover the distance be t hours.

then Ilya walks for t/2 hours and runs for t/2 hours

so , RS*t/2 + WS*t/2 = 5 miles

8.3*t/2 + 3.9*t/2 = 5

or t/2*(8.3+3.9) = 5

or t = 0.81 hours

or t= 0.81*60 mins = 49.1 mins

Ilyas average speed = 5/0.81 mph = 6.17 mph

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Added Tue, 29 Mar '16
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1

anya runs half of the track

t = d / s

t = 2.5 (Half the total distance) / 8.5 (speed of running)

This is .294 hours which is about 1058s...

And for the walking part...

t = d / s

t = 2.5 / 3.9

t = 2307s...

So you then add the two..

2307 + 1058 = 3365s = 56.09 minutes.

Therefore to work out the average speed, it is just distance / time...

(5 / 56.09)x60 = 5.3 mph

for llya

let it takes t time for her to cover the track

so for t/2 time she runs and for other t/2 time she walks.

for run

d1 = 8.3 x t/2

for walk

d2 = 3.9 x t/2

so d1+d2 = d = 5 miles

s0 6.1 x t = 5

t = 5/6.1 = 0.819 hours = 49.18 minutes (llya's time)

for llya's average speed

5/0.819 = 6.10 mph

Edit
Added Tue, 29 Mar '16
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