Problema Solution
Scott drives 80 KM an hour and Roberto drives 64 KM an hour starting at the same place but traveling in opposite directions. Scott starts 2 hours before Roberto. How many hours has Roberto been traveling when they are 376 KM apart?
Answer provided by our tutors
let
v1 = 80 km/h Scott's speed
v2 = 64 km/h Roberto's speed
t1 = the time that Scott travels
t2 = the time that Roberto travels
d = 376 the distance between them
Scott starts 2 hours before Roberto
t1 = t2 + 2
the speed = distance/time => distance = speed*time
since they travel in opposite directions we can write
Scotts distance traveled + Robertos distance traveled = the distance between them
using the formula speed = distance/time => distance = speed*time
v1*t1 + v2*t2 = d
80*t1 + 64*t2 = 376
by solving the system of equations
t1 = t2 + 2
80*t1 + 64*t2 = 376
we find
t1 = 3.5 hours
t2 = 1.5 hours
Roberto has been traveling 1.5 hours.