Problema Solution
Your aunt and uncle have been visiting your home. Five minutes after they drive away you realize they have forgot their luggage. You happen to know that they drive slowly, so you get in your car and drive to catch up with them. Your average speed is 10 miles an hour faster than their average speed, and you catch up with them in 25 minutes. How fast did you drive?
Answer provided by our tutors
let
v1 = the average speed of the your aunt and uncle
v2 = your average speed
Your average speed is 10 miles an hour faster than their average speed,
v2 = v1 + 10
you catch up with them in 25 minutes
25 min = 25/60 hours = 5/12 hours the time you traveled before catching up
25min + 5min = 30 min = 0.5 hours the time your aunt and uncle traveled before catching them up
v1*0.5 = v2*(5/12)
by solving the system of equations
v2 = v1 + 10
v1*0.5 = v2*(5/12)
we find
v1 = 50 miles/h
v2 = 60 miles/h
you drove 60 miles per hour.