Problema Solution
A bureau director has an appointment at 9 A.M. in a nearby province. If he travels at 40kph, he will arrive at 8 A.M.. If he drives at 30 kph, he will not arrive until 8:45 A.M. How far away is the province?
Answer provided by our tutors
let
d = the distance he travels
v1 = 40 kph
t1 = the time he travels the distance d with speed v1
v2 = 30 kph
t2 = the time he travels the distance d with speed v2
since 8:45 AM is 45 minutes after 8:00 AM follows
t2 = t1 + 45/60
t2 = t1 + 0.75
speed = distance/time => distance = speed*time
v1*t1 = v2*t2
40*t1 = 30*t2
plug t2 = t1 + 0.75 into the last equation
40*t1 = 30*(t1 + 0.75)
by solving we find
t1 = 2.25 h
click here to see the step by step solution of the equation
d = v1*t1
d = 40*2.25
d = 90 km
the province is 90 km away.