Need help solving Algebra word problems, please! :o)?

Question

I am almost finished with my math homework, but I am stuck on a few final word problems. Those who may help do not have to give me the answers if they do not wish to, but a push in the right direction would really help me! Please show me your work. Thank you so much to anyone who answers!

A freight train travels 90 miles in the same time that a passenger train travels 150 miles. If the passenger train goes 30 miles per hour faster than the freight train, find the rate of each. (I know RxT=D, but this one is stumping me...)

Sally walks to her friend's house at the rate of 3 miles per hour and then runs home at the rate of 6 miles per hour. How far does Sally live from her friend if the round trip takes 30 minutes?

How many liters of pure alcohol must be added to 20 liters of a 30% solution to obtain a 35% solution? (Is the answer 1.2 liters?)

If $10,000 is invested part at 7% and part at 9%, and if the total annual return is $840, how much was invested at 7%?

Answer 1

distance difference = 60
speed difference = 30

so time = 2 hours
thus speeds are 45mph and 75 mph


distance = d
time(1) = d/3
time (2) = d /6

0.5 = d/3 + d/6 = d(2 + 1)/6 = d (3/6) = d/2

d = 1 mile
(take care to have the speeds and the time in the same units)


(20.0.3 + x)/(20 + x) = 0.35
6 + x = 0.35(20 + x) = 7 + 0.35x
0.65x = 1
x = 1/ 0.65 = 1.538 litres (??)

a + b = 10,000
.07a + .09b = 840
so 7a + 9b = 84,000 = 7a + 9(10,000 - a) = 7a + 90,000 -9a = 90,000 -2a
2a = 6,000
a = 3,000
b = 7,000

checl 3,000.0.07 + 7,000.0.09 = 210 + 630 = 840

Answer 2

---------------------------F 90 mi
---------------------------------------------------------P 150 mi
The first one you need to somehow combine the equations to get rid of T since it is the same for both. Then you know the D's so put those in and for R use R for first the rate of the first train and (R + 30 mi/hr) for the passenger train. Sorry I don't know how to do first step, it been a long time.

For the second Sally would have taken 20 minutes to get there and 10 to get back. So three miles per 60 min for 20 min is how far? And 6 miles per 60 min for 10 min is how far?
3mi/60 min x 20 min =1 mile + 6mi/60 min x 10=1 so the answer would be 2 miles, but I think I didn't take the easy route to that answer

Hopefully some w/more knowledge can help you ;)!

Answer 3

P=150/T;F=90/T
distanceP/T=distance(F+60)/T
Vp=(Vfm/hr+30m/hr) Both equations are expressions of velocity,
hence are multiples of one another, in particular, the
time denominator, or .5 in the velocity formula. T then = 2 hours, Vp=75, Vf=45

Same distance both ways, so do simple average
3+6/2=4.5
4.5*.5/2=1.13miles

.30*20=6liters alcohol
.35*(20+x)=6+x
7+.35x=6+x
1=.65x
x=1.5liters add

840=8.4%
x*.07+(10000-x)*.09=840
900-.02x=840
.02x=60
x=3000
3000*.07+7000*.09=840

Answer 4

1) D/R = T is another way to write this.
90/Rf = 150/Rp
Rp = Rf + 30
90/Rf = 150/(Rf + 30)
90Rf + 2700 = 150Rf
Rf = 45

2)D/R = T
D/3 + D/6 = 30
3D = 180
D = 60

You can work the others :)

Answer 5

challenging factor lookup from bing and yahoo this might help