Problema Solution
Jeanie completed a 27 mile duathlon (race that is a combination of running and biking) in exactly 2 hours. She ran an average speed of 8.5 miles per hour and biked an average speed of 16 miles per hour. For how long did Jeanie bike during the race?
Answer provided by our tutors
let
x = the miles Jeanie biked
y = the miles Jeanie ran
t = 2 hours total time for the duathlon
d = 27 miles the distance she passed
v1 = 8.5 mph Jeanie's running speed
v2 = 16 mph Jeanie's biking speed
t1 = the time she biked
t2 = the time she ran
we will use the formula v = d / t that is
the average speed = the distance passed / the time needed
thus we can write the following system of equations
x + y = 27
x = 8.5 * t1
y = 16 * t2
t1 + t2 = 2
by solving it we find
t2 = 4/3 hours = 1 1/3 hour = 1 hour 20 min
Jeanie biked 1 hour 20 min.