Word Problems...?

Question

Two jets are traveling toward each other and are 4000 km apart. The rate of one jet is 100 km/h faster than the rate of the other. If the jets pass each other after 2.5 hours, what is the rate of the faster jet?

Also...
Ms. Driva Reck drove from her home to a service station at 48 km/h. She returned home by bicycle at 16 km/h. The entire trip took 4 hours. How far was the service station from Ms. Reck's home?

Also...
A plane on a search mission flew east from an airport, turned, and flew west back to the airport. The plane cruised at 300 km/h when flying east, and 400 km/h when flying west. The plane was in the air for 7 hours. How far from the airport did the plane travel?

FREE POINTS for anyone who attemps a good try. (10)

Answer 1

Let x be the rate of the faster jet, in km/h. Then the rate of the slower is x-100.

From now until the time they pass, the distance the faster jet travels is 2.5x, and the distance the slower jet travels is 2.5(x-100).

They started 4000 miles apart, so the total distance is 4000:

2.5x + 2.5(x-100) = 4000.

Multiply it out: 2.5x + 2.5x - 250 = 4000, or 5x = 4250, so x=850 km/h.

Second problem:
Let d be the distance to the station. Then the time taken getting there is d/48, and the time getting back is d/16. You have d/48 + d/16 = 4, so d(1/48 + 1/16) = 4. 1/48 + 1/16 = 1/12, so d=48 km.

Third problem:
Let d be the distance from the airport to the turnaround point. Then the time flying east is d/300, and the time flying west is d/400. You have d/300+d/400=7, so d(1/300+1/400)=7. 1/300 + 1/400 = 7/1200, so d(7/1200)=7. Therefore d=1200 km.

Answer 2

Word Problems...?
Two jets are traveling toward each other and are 4000 km apart. The rate of one jet is 100 km/h faster than the rate of the other. If the jets pass each other after 2.5 hours, what is the rate of the faster jet?

let A be speed of 1st plane & B be speed of 2nd.
A=B+100
2.5=4000/(A+B)=4000/(B+B+100)
2.5/4000=1/(2B+100)
2B+100=4000/2.5=1600
2B=1500
B=750 kph
A=B+100=750+100=850 kph

Check
4000/(850+750)=4000/1600=40/16=5/2=2.5

Also...
Ms. Driva Reck drove from her home to a service station at 48 km/h. She returned home by bicycle at 16 km/h. The entire trip took 4 hours. How far was the service station from Ms. Reck's home?

let he distance =x
x/48+x/16=4
x+3x=48*4=192
4x=192
x=192/4=48 km

Also...
A plane on a search mission flew east from an airport, turned, and flew west back to the airport. The plane cruised at 300 km/h when flying east, and 400 km/h when flying west. The plane was in the air for 7 hours. How far from the airport did the plane travel?

let x=distance
x/300+x/400=7 multiply by 1200
4x+3x=7*1200=8400
7x=8400
x=8400/7=1200 km

Answer 3

The faster is flying as speed of 850 Km and the other one at speed of 750..
Driva - 48 km;
Plan - 1200 km

Answer 4

What shapes do you get when you split the square with a diagonal? Two trangles. Since we know the field is a square, that means all the sides are equal (therefore, if you know one side, you know all the sides). So now you have a trangle with two sides equal to 60 feet. You can now use Pythagorean's theorem: A (squared) + B(squared) = C (squared) A and B are your two sides and then you just solve for C. Good luck!

Answer 5

1)850 km/h
2)48 km
3) displacement=0
distnace travelled=2400km

Answer 6

1. 1600 Kilometres per hour

2. 128 Kilometres away

3. 2450 Kilometres total traveled

Answer 7

Get a tutor.

Answer 8

i wish i knew this answer but i couldn't even figure it out when my teacher gave it too us.