Question

Ilya and Anya each can run at a speed of 7.80 mph and walk at a speed of 3.60 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.a)How long does it take Anya to cover the distance of 5.00miles ?Express your answer numerically, in minutes.b)Find Anya's average speed.Express Anya's average speed save,Anya numerically, in miles per hourC)How long does it take Ilya to cover the distance?Express the time tIlya taken by Ilya numerically, in minutes.d)Now find Ilya's average speed.Express Ilya's average speed save,Ilya numerically, in miles per hourExpress Ilya's average speed save,Ilya numerically, in miles per hour.

Answer 1

Answer:

(A)60.6 mins

(B)4.95 mph

(C)52.8 mins

(D) 5.68 mph

Explanation:

distance (d) = 5 miles

walking speed (Sw) = 3.6 mph

running speed (Sr) = 7.8 mph

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

From the question, Anya walks half of the distance and runs the other half, hence we can deduce that:

• Anya walks for 5/2 = 2.5 miles at a speed of 3.6 mph

       Hence Anya walking time = distance/ speed = 2.5/3.6 = 0.69 hr

• Anya runs for 5/2 = 2.5 miles at a speed of 7.8 mph

       Hence Anya running time = distance/ speed = 2.5/7.8 = 0.32 hr

• Total time taken by Anya to cover 5 miles = 0.69 + 0.32 = 1.01 hr

         = 1.01 x 60 = 60.6 mins

(B) Find Anya's average speed

 average speed = distance / time

average speed = 5 miles / 1.01 hr = 4.95 mph

(C) How long does it take Ilya to cover the distance?

From the question,  Ilya walks half of the time and runs the other half. hence we can deduce that:

• Let's assume it takes Ilya T hours to cover the 5 miles, hence Ilya walks for T/2 hours and runs for T/2 hours
• The distance Ilya covers walking = walking speed x time = 3.6 x (T/2)

• The distance Ilya covers running = running speed x time = 7.8 x (T/2)
• Total distance = walking distance + running distance
• 5 = 3.6(T/2) + 7.8(T/2)

        5 = (3.6 + 7.8) (T/2)

        10 = 11.4(T)

         T = 10 / 11.4 = 0.88 hour

         T = 0.88 x 60 = 52.8 mins

(D)  Find Ilya's average speed

 average speed = distance / time

average speed = 5 miles / 0.88 hr = 5.68 mp