Question

Ilya and Anya each can run at a speed of 8.80mph and walk at a speed of 3.70mph . 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 5.00 miles? Express your answer numerically, in minutes.

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

C. How long does it take Ilya to cover the distance? Express the time taken by Ilya numerically, in minutes.

D. Now find Ilya's average speed. Express Ilya's average speed numerically, in miles per hour.

Answer 1

let Var and Vaw be run walk speed of anya
let Vir an Viw be run and walk speed of illya
Var = Vir = 8.8mph
Vaw = Viw = 3.70mph
distance = 5.0 miles
for anya
time taken while running = distance/2xVar
                         = 5/2x8.8
                         =17.045 min                   
time taken while walking = distance/2XVaw
                         = 5/2x3.7
                         = 0.6757 hrs
                         = 40.541 minutes
total time taken = 17.045 + 40.541
                 = 57.586 minutes
average speed = total distance / total time
              = 5 x 60/57.586
              = 5.2096 mph
for illya
let k be the distance travelled during running
time taken for running = distance /Vir
                       =k/8.8
time taken for walking = distance/Viw
                       = 5-k/3.7
time taken for runnning = time taken for walking
k/8.8 = 5-k/3.7
k(3.7 + 8.8) = 5 x 8.8
k = 3.52
time taken for running = k/8.8
                       = 3.52/8.8
                       = 0.4 hrs
                       = 24min
total time taken = 2 x 24 = 48min
average speed = total distance /total time
              = 5x 60/48
              = 6.25mph

a 57.586minutes
b 5.2096mph
c 48min
d 6.25mph