SOLUTION: 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.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F%28%28s-10%29%29 - 360%2Fs = 3
multiply the equation by s(s-10)
s(s-10)*360%2F%28%28s-10%29%29 - s(s-10)*360%2Fs = 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