The distance between towns M and N is 280 km. A car and a lorry travel from M to N.
The average speed of the lorry is 20 km/h less than that of the car. The lorry takes 1 h 10 min more than the car to travel from M and N.
(a) If the speed of the lorry is x km/h, find x
(b) The lorry left town M at 8: 15 a.m. The car left town M later and overtook the lorry at 12.15 p.m. Calculate the time the car left town M.
speed of lorry ---- x km/h
speed of car ----- x+20 km/h
time for the car = 280/(x+20)
time for lorry = 280/x
280/x - 280/(x+20) = 70/60
divide by 70
4/x - 4/(x+20) = 1/60
times 60x(x+20), the LCD
240(x+20) - 240x = x(x+20)
240x + 4800 - 240x = x^2 + 20x
x^2 + 20x - 4800 = 0
(x - 60)(x + 80) = 0
x = 60 or x is a negative
the speed of the lorry is 60 km/h
b) at the time of overtaking, the lorry had gone for
4 hrs, thus it had gone 240 km
for the car to go those same 240 km would have taken 240/80 hrs or 3 hrs.
So just "backup" 3 hrs from 12:15