Ilya and Anya each can run at a speed of 8.30mph and walk at a speed of 3.90mph

Question

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.

Explanation / Answer

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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