K, here I go again..My bad..?

Question

A cyclist traveled at a rate of 24 mph to visit a nearby town. The cyclist averaged 18 mph on the return trip. If the round trip took 4.9 hours, find the distance to the nearby town. [Ten points for the correct algebra equation and five points for solving the equation.

Answer 1

how about 2 points for answering?
oh thats right, you have no control over that.
and how are you going to dole out 5 points?
you make it sound like you're doing US a favor.
how about:
you = doing your own homework.

Answer 2

OK...it isnt as bad as it looks. I will help you set up the equation, but I wont solve it for ya (that takes all the fun out of things!)

OK

here is what we have

distance, and rates. but we dont know the times

we know that the distance in both sides of the trip was the same. and we know that the total time was 4.9 hours.

SO, start with the trip TO the town. D=RT but, we dont know T. and we dont know D. . bu we know R (R=24)
So, D=24T

Now the return trip
Distance is the same...(am using small letters this time to show that they are different values, since distance is the same, we can use the big D again)
D=rt so D=18t

OK, so far, no dice, righ? OK, BUT, we do know the TOTAL time for the trip was 4.9 hours...in other words. . the time to go TO town and the time to return FROM town add up to 4.9

so T+t=4.9 OR, if we get one of the letters by itself (let's get little t by itself). . we can say that t=4.9-T
hey, now we have something

look back. . we have D=24T and we have D=18t
so that means that 24T=18t. ..

AND, since t=4.9-T, we can plug that in and we get
24T=18(4.9-T)
from there, solve to find T..that will get you the time for the trip to town.
And, since you are looking for distance. . after you find the T,
go back and plug in (D=RT. . .D=24T. . )

I hope this helps!! (Just getting you set up, though. . .I know, I am cruel. . . I am sure plenty of other people will do the whole thing. If you are still stuck at this stage, let me know, and I will walk you through the rest of it. But usually, the set up is the hardest part)..Oh man, i did do that the hard way. . .SORRY!! I over thinkeded it!

Answer 3

If the distance is x miles, the trip there took x/24 hours and the trip back took x/18 hours. So we have
x/24 + x/18 = 4.9
Multiply through by 72 (LCM of 24 and 18) to get
3x + 4x = 352.8
<=> x = 352.8 / 7 = 50.4.
So the town is 50.4 miles away.

Answer 4

Let x = distance to the nearby town.

x/24 + x/18 = 4.9
7x/72 = 4.9
7x = 4.9 * 72
7x = 352.8
x = 352.8/7
x = 50.4

The answer is 50.4 miles.

Proof:
(50.4/24) + (50.4/18)
2.1 hours forth + 2.8 hours back =4.9 hours total

Answer 5

d = 24 * t1= 18 * t2
t1 + t2 = 4.9 = d/24 + d/18 = d(1/24 + 1/18) =d*7/72

d = 4.9 * 72/7 =50.4