Need help with algebraic problem?

Question

... and explain how you did it?

Two cars are leaving from the same point and are travelling in opposite directions. One is giong 10 km per hour faster than the other is. After travelling two hours, they are 160 km apart. How fast is each car travelling?

Answer 1

suppose 1st car spped is x
then other car speed become x+10
now , they are in opposite direction so in 1 hr they will x+x+10 km apart
so in 2 hrs they will 2(x+x+10) km apart
so, 2(x+x+10)=160
2x+10=80
x=35

so, one car speed is 35km/hr and other one is 45km/hr

Answer 2

Lets the slow car have a speed x . the quickest has the speed x+10 after two hours the first deplaced 2x and the second 2(x+10) =2x+20
the distance between them is equal to 2x+2x+20=160

4x+20=160---> 4x =140 x=35

the slow x=35 , the other x=35+10=45

Proof 35*2 =70 km 45*2 =90 km and sum 70+90=160

Answer 3

The slow one is going at 35 km/h, the fast one at 45km/h.

You work it out like this:

160 = 2(a+10)+2a

160 is the distance and the twos are the number of ours of travel, i.e. the one car has been travelling 10kmh faster for two hours is shown in the first bracket added to the distance that the other car has travelled in the same time. Next we get rid of the brackets by multiplying everything inside them by the number outside them (i.e. the two hours)

160 = 2a+20+2a

Next we simplify it by adding together the bits that are in the same units (in this case 'a' and plain numbers)

160 = 4a+20

Then we get rid of 20 from both sides to simplify it further.
160 - 20= 4a

So now we know four lots of 'a' = 140. So we divide both sides by four to get the value of one a.

140=4a
35=a

But the faster car travels at a+10, so that's 45.

Then I drew it out to check it.

2*45 + 2 *35 = 160. So it's right. Hope this helps, do an edit on your question to let me know if you don't get it and I'll try and explain it another way.

Answer 4

Assume speed of the 1'st car to be x km/hr . Hence speed of the second car will be (x+10) km/hr .
distance travelled by the first car in 2 hrs.= 2x
Distance travelled by the second car in 2 hrs. = 2*(x+10)
if you are provided with distance between those two cars when they just started moving (for instance let it be
'a') then you will get equation like the following:-
a + 2x + 2(x+10) = 160
if you solve it further you will get the answer . So check your question & best luck

Answer 5

Let x be the speed of the slower car.

The distance travelled by the slower car:
2x
The distance travelled by the faster car:
2(x+10)

Total distance travelled=160km
160=2x + 2(x+10)
160=2x + 2x + 20
160 - 20= 4x
4x = 140
x = 140/4= 35 km/hour

The speed of the slower car= 35 km/hour
The speed of the faster car= x+10= 45km/hour

Hope that solves the problem :D

Answer 6

Let the speed of one car =v km. /hr
Speed of other car = (v + 10) km. / hr.
Distance travelled by the first car in 2 hours = 2 v km.
Distance travelled by second car in 2 hours = (v + 10) 2 km.
Total distance travelled = 2 v + (v + 10) 2 =160 km.
ie. 2v + 2v +20 = 160
4v = 140 ; v = 35
Therefore tthe speeds of the cars are 35 km/ hr. & 45 km./ hr.

Answer 7

let

x = speed of first car

x + 10 = speed of second car

2 = time traveled

160= distance traveled

- - - - - - - - - - - - - - -

2(x) + 2(x + 10) = 160

2x + 2x + 20 = 160

4x + 20 = 160

4x + 20 - 20 = 160 - 20

4x = 140

4x/4 = 140/4

x = 140/4

x = 35

The speed of the first car is 35

The speed of the second car is 45

- - - - - - - - - - -s-

Answer 8

xkm/hour<--------- 0 --------->(x+10)km/hour

the distance after 2 hours
(x+(x+10))*2=160
4x+20 =160
x = 35

Answer 9

the speed of car 1 = s1
the speed of car 2 = s2= s1+10
car 1 made (x1) km by 2 hours
car 2 made (x2) km by 2 hours.
velocity = distance / time
x1= s1 *2
x2 = s2 *2, or = (s1+10)*2
x1+x2=160= (s1*2) + ((s1+10)*2)
S1=35km/h
s2=35+10=45km/h
Thank you....

Answer 10

speed of a be v
speed of b will be v+10
concept of relative speed says
2(2v+10)= 160
2v+10=80
2v=70
v=35