Question 936925
a bus travels 10 kph faster than a truck.
 It travels 360 km in 3 h less time than the time required by the truck to travel the same distance.
 Find the rate of each.
:
let s = the speed of the bus
then
(s-10) = the speed of the truck
:
Write a time equation, time = dist/speed
;
Truck travel time - bus travel time = 3 hrs
{{{360/((s-10))}}} - {{{360/s}}} = 3
multiply the equation by s(s-10)
s(s-10)*{{{360/((s-10))}}} - s(s-10)*{{{360/s}}} = 3s(s-10)
cancel the denominators and you have
360s - 360(s-10) = 3s(s-10)
360s - 360s + 3600 = 3s^2 - 30s
Combine on the right to form a quadratic equation
0 = 3s^2 - 30s - 3600
simplify divide the 3
s^2 - 10s - 1200 = 0
Factors to 
(s-40)(s+30) = 0
the positive solution
s = 40 km is the speed of the bus
You find speed of the truck