30(x- 15)=20(x+5)
30x-450=20x+ 100
30x-20x= 100+450
10x=550
x=55
Five minutes in advance, the speed of the motorcycle
(55- 15)×30÷(55-5)
=40×30÷50
= 1200÷50
=24
A: If you plan to arrive five minutes early, the speed of the motorcycle should be 24 kilometers per hour.
7. Let the original 40% brine be x grams and the original 10% brine be y kilograms.
40%x+ 10%y=30%(x+y)①
40% x+ 10% y+300×20% = 25%(x+y+300)②
① Simplified calculation is 0.4x+0.1y = 0.3x+0.3y..
0.4x-0.3x=0.3y-0. 1y
0. 1x=0.2y
x=2y③
② The simplified calculation is 0.4x+0.1y+60 = 0.25x+0.25y+75.
0.4x+0. 1y-0.25 x-0.25y = 75-60
0. 15x-0. 15y = 15
x-y= 100④
③ Substitute into ④ to get 2y-y= 100.
y= 100
x=2× 100
x=200
A: The original 40% salt solution is 200 grams.
8. Suppose that the working hours for making 1 shirts are x, the working hours for making 1 pants are 2x and the working hours for making 1 tops are 3x.
2x+3×2x+4×3x= 10
2x+6x+ 12x= 10
20x= 10
x=0.5
2x= 1
3x= 1.5
14×0.5+ 10× 1+2× 1.5
=7+ 10+3
=20
Answer: It takes 20 working hours to make 14 shirts, 10 pants and 2 tops.
10. Let AB be x kilometers apart.
x = 1/3(x/2+50)+400+ 1/2[ 1/3(x/2+50)+400-(x/2+50)]
6x = 2(x/2+50)+2400+3[ 1/3(x/2+50)+400-(x/2+50)]
6x = x+ 100+2400+(x/2+50+ 1200-3(x/2+50)
6x-x = 2500+x/2+ 1250-3x/2- 150
5x=3600-x
5x+x=3600
6x=3600
x=600
A: AB is 600 kilometers apart.