just a little thing that I don't understand?

Question

the distance between A and B is 100 km .
B is east of A.
2 vehicles start travelling at the same time,one from A and the other from B.
Both go east.
they meet after 10 hours.
the vehicle that started from B goes 4 km in (t+2 minutes) time when the vehicle started at A goes 4 km in t time.
what are the speeds of the 2 vehicles?


I got this:

4=(x+10)*(4/x+2/60)
the answer should be
4=(x+10)*(4/x-2/60)

this is the equation for B so why do I subtruct 2 minutes and not add them?

Answer 1

what i got was car that left pointa was going 25km per hour
and car at point b was going 15km per hour
carA 25(10)
carB15(10)
carA250km
carB150km
both heading east and a is 100km west of b so
carA went 250km minus dis. between a-b which is 100km so both car A and B went 150 km east of point b

Answer 2

Drawing a little sketch will help you.

Write equations for distance travelled in 10 hrs:

car b:
d = Vb*10

car a:
d+100 = Va*10

combine:
Vb*10+100 = Va*10
or
Va-Vb = 10

Now use the expressions for velocity, take care to convert the minutes into hours:

4/(t/60) - 4/[(t+2)/60] = 10
simplify:
480/[t(t+2)] = 10
t^2 +2t - 48 = 0
this has roots +8, -6; the positve one is correct:

So,
A goes 4 km in 8 minutes or
4*60/8 = 30 km/hr

you can get B easily with
Va-Vb = 10 and so Vb = 20 km/hr

now check:
Va*10 = 300 km
Vb*10 = 200 km

the difference, 100 km, is the distance between A and B.

+add
Como is correct about the roots to the quadratic.
They are -8 and +6. I mistakenly used +8 and -6.

Correcting my calcs:

Va = 4km/6min = 40 km/hr
and
Vb = Va-10 = 30 km/hr
or
Vb = 4km/(6+2)min = 4*60/8 = 30 km/hr

the check gives the same 100 km A to B separation.

Nice work, como.

Answer 3

B speed = 4/ (t + 2) km / min
A speed = 4 / t km / min
Relative speed of A to B is:-
4 / t - 4 / (t + 2) km / min
(4t + 8 - 4t) / t (t + 2) km / min
= 8 / [ t (t + 2) ] km / min
Meet after 600 mins
t = distance / speed
600 = (100 t) (t + 2) / 8
4800 = (100 t) (t + 2)
48 = t² + 2t
t² + 2t - 48 = 0
(t + 8) (t - 6) = 0
t = 6 mins
B speed = 1 / 2 km / min = 30 km / h
A speed = 4 / 6 km / min = 40 km / h