Problema Solution
A bus goes from town A to B in an exact time. If the bus goes at the rate of 50km/h, then it will arrive B 42min later than it had to and if it increases
its speed 5.5/9 m/sec., it will arrive B 30min earlier. Find:
A) The distance between the two towns;
B) The exact time that it takes to arrive town B
C) The speed of the bus(by schedule) for the exact time.
Answer provided by our tutors
let
v = the speed of the bus (by schedule) for the exact time
d = the distance between the two town
t = the exact time that it takes to arrive town B
since v = d/t we have d = v*t
50(t + 42/60) = vt
5.5/8 m/sec = 5.5*60*60/(8*1000) = 2.475 km/h
(50 + 2.475)(t - 30/60) = vt
by solving the equation:
50(t + 42/60) = (50 + 2.475)(t - 30/60)
we find:
t = 24.74 hr is the exact time that it takes to arrive town B;
click here to see the step by step solution of the equation:
d = 50(t + 42/60)
d = 50(24.74 + 42/60)
d = 1,272 km is the distance between the two towns;
v = d/t
v = 1272/24.74
v = 51.41 km/h the speed of the bus(by schedule) for the exact time;