# 1. A car travels 20 kph faster than a truck. The car covers 350 km in two hours less than the time it takes the truck to travel the same distance. What is the speed of the car? How about the trucks?2. Jane and Maria can clean the house in 8 hours if they work together. The time that Jane takes in cleaning the house along is 4 hours more than the time Maria takes in cleaning the same house. How long does it take Jane to clean the house alone? How about Maria?

1
by JohnRey13

2014-09-16T22:44:54+08:00
1.) Let s = the speed of the truck
and (s+20) = the speed of the car

to get the time of each vehicle time = distance/ speed
truck time = 350/s
car time = 350/(s+20)

Truck time - car time = 2 hrs so,
(350/s) - [350/(s+20)] = 2
LCD we can get
[350(s+20) - 350s]/s(s+20) = 2
then transpose the denominator
350(s+20) - 350s = 2s(s+20)
simplifying  we can get
350s + 7000 - 350s = 2s^2 + 40s
then simplify more to become quadratic equation
2s^2 + 40s - 7000 = 0
to make it simplest divide the equation by 2
s^2 + 20s - 3500 = 0
by factoring we can get
s= 50
s= -70 (impossible because of the sign)

so
s = 50 km/h is the speed of the truck
s + 20 = 70 km/h is the speed of car