The first team of workers received 50 kg of cement less than the second team. for every hour of work the first team was using 150 kg of cement, while the second team was using 200 kg. in three hours the first team had 1.5 times as much remaining cement as the second team. how much cement was delivered to each team of workers?

There are 2 unknown terms in this problem 
the amount of cement the first team received is termed as 'x' hereafter 
the cement the second team received is termed as 'y'
the first team received 50 kg less, the 1st equation is as follows;

x = y - 50    after rearranging 
1) x-y = -50
for every hour 150 kg and 200 kg were used by the two teams separately 
after three hours first team used up 150*3 = 450 kg
the second team used up 200 * 3 = 600 kg
however the first team had 1.5 times as much as second team had after three hours. 
After three hours;
the amount second team had leftover was y - 600
the amount first team had leftover was x - 450
 the amount the second team had ,multiplied by 1.5 is equal to what the first team had
we can build the 2nd equation using this information

1.5 * (y-600) = x-450
1.5y - 900 = x - 450 
rearrange the equation,
 
 1.5y - x = -450 +900
2) 1.5y - x = 450 

add 1st and 2nd equations to eliminate x 
1) + 2)     (x - y = -50) + (1.5y - x = 450)
1.5y - y = 450 -50
0.5y = 400
y = 400/ 0.5
y = 800 kg
substitute y = 800 in x = y - 50
x = 800 - 50 
x = 750 kg

first team received 750 kg and second team received 800 kg