Problema Solution
During a hurricane evacuation from the east coast of Georgia, a family traveled 230 miles west. For part of the trip, they averaged 70 mph but as the congestion got bad, they had to slow to 20 mph If the total time of travel was 7 hours, how many miles did they drive at the reduced speed?
Answer provided by our tutors
let
d1 = the miles traveled in with average speed v1 = 70 mph
t1 = the hours traveling with avg. speed v1
d2 = the miles traveled with average speed v2 = 20 mph
t2 = the hours traveling with avg. speed v2
a family traveled 230 miles
d1 + d2 = 230
the total time of travel was 7 hours
t1 + t2 = 7
since avg.speed = distance/time -> time = distance/avg.speed
t1 = d1/v1 = d1/70
t2 = d2/v2 = d2/20
lets plug t1 and t2 in t1 + t2 = 7 and we get
d1/70 + d2/20 = 7
by solving the system of equations
d1 + d2 = 230
d1/70 + d2/20 = 7
we find
d1 = 126 miles
d2 = 104 miles
click here to see the step by step solution of the system of equations
they drove 104 miles at the reduced speed of 20 mph.