Problema Solution
It takes 4.5 hours for a ship moving downriver to get from port A to port B. The return journey takes 6.3 hours. The river flows at 40 meters per minute. What is the distance between the two ports?
Answer provided by our tutors
let
t1 = 4.5 hr the time of the travel downriver from A to B
t2 = 6.3 hr the time of the return journey
r = 40 meters per min = (40/1000)/(1/60) km per hr = 2.4 km/hr
v = the speed of the sip in still water
d = the distance between the two ports
since speed = distance/time follows distance = speed*time
going downriver the speed of the ship is: v + r
d = t1(v + r)
d = 4.5(v + 2.4)
going upriver (the return journey) the speed of the ship is: v - r
d = t2(v - r)
d = 6.3(v - 2.4)
by solving the system of equations:
d = 4.5(v + 2.4)
d = 6.3(v - 2.4)
we find:
d = 75.6 km
click here to see the step by step solution of the system of equations:
the distance between the ports is 75.6 kilometers.