Hard algebra problems, involving speed, distance and time? Please help!!?

Question

1) A girl runs at a constant speed for T minutes to run M km. How long, in seconds, will it take her to run N km if she runs at the same speed?

2) A cyclist travels M km at V km/h and N km at U km/h. The average speed of the cyclist is?

3) A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

Thanks!!

Answer 1

1)
speed
= M/T km per min
= (M/T)(1/60)
= M / (60T) km per sec

Time
= distance / speed
= N / (M / 60T)
= N * (60T / M
= (60 NT) / M

2)
Total Distance = M + N
Total Time = (M/V) + (N/U)

Average speed
= (total Distance) / (total Time)
= (M + N) / (M/V + N/U)

3)
Right now:
Boy = x
Sister = x + 3

Three years ago:
Boy = x - 3
Sister = (x + 3) - 3 = x

(x - 3) = (2/3)(x)
3(x - 3) = 2x
3x - 9 = 2x
x = 9

Boy is now 9 and sister is now 12

Answer 2

Question 1
Speed = M/T km/minute
t = distance / speed
t = N / (M/T) minutes
t = NT / M minutes
t = 60 NT / M seconds

Question 2
Distance = (M + N) km
t1 = M / V hours
t2 = N / U hours
Total time = M/V + N/U
Average speed
(M + N) / [ M/V + N/U]
(M + N) / (MU + NV) / (VU)
(VU).(M + N) / (MU + NV) km / h

Question 3
NOW
sister = x years
boy = x - 3 years
3 YEARS AGO
sister was x - 3 years
boy was x - 6 years
x - 6 = (2/3).(x - 3)
3x - 18 = 2x - 6
x = 12
Present Ages
Girl is 12 years
Boy is 9 years

Answer 3

1)speed v=M/60T
time for Nkm=N/v=Nx60T/M=60NT/M answer
2) total time of cycling t=M/V+N/U=(MU+NV)/UV.
total distance=M+N
his average speed=(M+N)xUV/(MU+NV)=UV(M+N)/MU+NV. answer
3)let the boys age be x, his sister's age is x+3
x-3=2/3x
x/3=3
x=9.
boys age is 9 and his sister's age is 12years. answer

Answer 4

1) v=const
s1=m
t1=t
s2=n
v1=v2
_____
v1=s1/t1= m/t
v1=v2=s2/t2
t2=s2/v2=n/(m/t)= (n*t)/m


3)b-boy , s-sister
b+3=s
b-3=2/3(s-3)
_________________
s=12,b=3