10pt for nasty word problem? help ;(?

Question

A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?

Answer 1

My teacher gave my class two websites that help you ALOT 8)

www.hotmath.com

www.smarthinking.com

hope i helped :)

IF those dont work out--

try googling a free tutoring website,where someone could help you LIVE xD just find a safe one :) the above two,are tutoring websites also,and are very safe (:

Answer 2

Make some variables, and things start to get less nasty.

Let:

d = distance from X to Y (the thing we're trying to answer)

t_xy = time to get from X to Y

t_yx = time to get from Y to X

> "...travels from Town X to Town Y at an average rate of 50 mph..."

This means:

d / t_xy = 50 mph

> "...returns at an average rate of 40 mph..."

This means:

d / t_yx = 40 mph

> "He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph."

This is a long sentence, so let's break it down.

"He takes a 1/2 hour longer.."

They're talking about his normal round trip, which take a time of t_xy + t_yx.  So they're saying that "t_xy + t_yx is 1/2 hour longer than" something.

"...he would take if he made the round trip at an average of 45 mph."

So "t_xy + ty_x is 1/2 hour longer than T", where T is the length of this hypothetical 45mph trip.  (We just made another variable).

So that sentence in math is:

t_xy + t_yx = 1/2 + T

Now, before we go farther, notice that:

(2d) / T = 45 mph

or:

T = (2d) / 45

So combine that with the previous equation:

t_xy + t_yx = 1/2 + (2d) / 45

Next, remember these from above:

d / t_xy = 50 mph

d / t_yx = 40 mph

So we can substitute "d / 50" for t_xy and "d / 40" for t_yx:

d/50 + d/40 = 1/2 + (2d) / 45

Now there's just one variable "d" in that equation; so solve for "d".

Answer 3

120

speed x time = distance

40=x(distance)/t+30(time + 30 because it takes him an extra half an our tan 45mph)

45=x/t

45t=x

40=45t/t + 30

40t + 120 = 45t

t=24

plug 24 in for t in any equation and solve for d

d=120

Answer 4

Let  the distance from Town X to Town Y be d.

time = distance / speed

t=d /50 + d/40

Half an hour more with 45 mph  both ways.

t+1/2 = 2d / 45

2d/45 +1/2 = d/50+d/40

4000d+45000=1800d+2250d

-50d=-45000

d=900 miles

Answer 5

wait a minute, if you go there at 50 and come back at 40 doesn't that average out to 45 round trip anyways?

Answer 6

Distance= Rate x Time, so Time=Distance/Rate

D/50+D/40=(2D/45)+.5

D=900 miles

Answer 7

Hi,

distance/rate to + distance/rate from - ½ = distance/ave rate

x... ....x.... 1..  ..2x

---.+.----.-.--- = -------

50.. .40.. .2.. ...45

Multiply every term by 1800 to cancel out denominators. then solve for x.

36x + 45x - 900 = 80x

81x - 900 = 80x

x = 900

It is 900 miles from town X to town Y. <==ANSWER

I hope that helps!! :-)

Answer 8

x/50 + x/40 = 2x/45 + 1/2

x + 50x/40 = 100x/45 + 25

40x + 50x = 4000x/45 + 1000

1800x + 2250x = 4000x + 45000

50x = 45000

x = 900 miles

Answer 9

d1 = d2

d1 = 50t1

d2 = 40t2

t2 = (1/2) + t1

Avg. = (d2 - d1)/(t2 - t1)

t2 = (5/4)t1

45 = [50(5/4)t1 - 50t1]/(1/2)

90 = (1/4)(50t1)

360 = 50t1

7.2 = t1

d1 = 50(7.2) = 360

Therefore, the distance is 360 miles.

Answer 10

time=distance x rate

I'd guess I'd set it up like this, I'll keep trying to solve if there isn't an answer.

t=2d*45

(d*50)+(d*40)=1.5t

(d*50)+(d*40)=1.5(2d*45)

d*50+d*40=3d+67.5