The Grass Doctor

Grade 9 math word problem help?

1. Gregor is planning a driving trip. Part of his trip will be along major highways and part will be along country roads or on city streets. The speed limit on the highways in 100km/h while the limit on the roads in 60km/h. The total time he wants to spend driving is 12h and he has to travel 850km.How much time is he going to spend on each road? 2. Eve operates an apple farm. She spreads a mixture of a fertilizer called "all grow" and a weed suppresant "no weed" around her trees each autumn. She spent $800 this autumn to fill the spreader. All grow costs $2.50/kg and no weed costs $5.00/kg. Her spreader holds 200kg of mixture. How much of each did he use?

Public Comments

1. 1) not enough information.
2. x=time on highway y=time on roads 100x + 60y = 850 x + y = 12 y = 12-x 100x+60(12-x)=850 100x+720-60x=850 40x=130 x=13/4=3.25 hours y=8.75 hours x=kg of All Grow y=kg of No Weed 2.5x+5y=800 x+y=200 y=200-x 2.5x+5(200-x)=800 2.5x+1000-5x=800 -2.5x=-200 x=80 kg y=120 kg
3. 1. What a silly question. 850 = 100*H + 60*(12-H) The 850 represents the total distance traveled. The 100*H represents the distance traveled on the highway. H is "time in hours" spent on the highway. The 60*(12-H) represents the distance traveled on the side roads. He goes 60 km/h, and has to spend (12-H) hours there. This is because the question said the total time on both roads must be 12 hours. 850 = 100*H + 60*(12-H) 850 = 100H + 720 - 60H 130 = 40H H = 3.25 on the highway 12 - H = 8.75 on the back/country roads. What a waste of gas. He could have gotten there in 8 hours. (2) I'm sick of doing your homework now. Have fun!
4. 1. Simultaneous equations: 100x + 60y = 850 x + y = 12 Solve by substitution. 2. None. 'He' contradicts 'she'. In the case you meant 'she' instead of 'he' in the last sentence, then simply resolve the two simultaneous equations: 2.5x + 5y = 800 x + y = 200 by substitution.