Adrain and Bala decided to go on a cycling expedition.Both of them chose different routes to the destination.Adrain travelled by rooute A,which is 120km long,at an average speed of xkm/h.Bala chose route B,which is 5km shorter,but has more challenging terrain.He covered the distance at an average speed of 2km/h slower than Adrain.
Qn:Given that Bala arrived at the destination 40 minutes later than Adrain,form an equation in x.


I'm really bad at maths,especially speed problems,anyone can help me out?

Since x is Adrian's rate, then Bala's rate is x-2.

The time Adrian made it is t, then Bala made it in t+2/3 hours.

d=rt

Adrian: 120=xt

Bala: 115=(x-2)(\frac{120}{x}+\frac{2}{3})

Solve for x

Bala:115=(x-2)(120/x+2/3)
=(360+2x)/3x
Is it = (360x-720+2xsquare-4x)/(3xsquare-6x) ?

I'm not sure because from here on the answer is different from the one given.

The answer I get is 343xsquare-1046x-720=0
while the correct answer is 2xsquare+11x-720=0

Try again then. Because it comes out to 2x^{2}+11x-720=0

Multiply through by the LCM, which is

3x(x-2) and cancel terms accordingly.

Here's how I do it:
115=(x-2)(120/x+2/3)
120/x + 2/3 = 360+2x/3x
(360+2x/3x)(x-2)
=(354x-720+2xsquare)/(3xsquare-6xsquare)

115/1 = (354xsquare-720+2xsquare)/(3xsquare-6x)

115(3xsquare-6x)=(354xsquare-720+2xsquare)

345xsquare-690x-354xsquare-720-2xsquare=0

-11xsquare-690x-720=0

I had done it about 3 times,but the answer I get is still this.I checked but I think all the steps I had done are correct?

Here's how I do it:
115=(x-2)(120/x+2/3)
120/x + 2/3 = 360+2x/3x
(360+2x/3x)(x-2)

This whole thing isn't working. When you multiplied the 3x by the (120/x + 2/3), the 3 cancels out on the second term and the x doesn't end up in the denominator:

(3x)\ \left(\frac{120}{x}\ +\ \frac23\right)

Or, so you can visualize it more easily:

(3x)(\frac{120}{x})\ +\ (3x)(\frac23)

On the left term the x cancels, which you did correctly. But on the right, the 3's cancel so that denominator disappears, and the x goes in the numerator:

(3\cancel{x})(\frac{120}{\cancel{x}})\ +\ (\cancel{3}x)(\frac{2}{\cancel3})

You also missed the extra (x - 2). If you're multiplying through by (3x)(x-2) then you've got that extra (x-2) in there as well. You've only used the 3x. (I think - honestly I'm having a hard time following what you're doing.)

Try to fix those and go from there.

I did it a different way, which for me was a heck of a lot easier, not to mention easier for my mind to think up. I can't say as I understand the LCD in that situation, other than I got it to work out to the same thing by doing it.

I FOILed the right side first, and then multiplied both sides by 3x.

Oh, and used a ^ (carrot) for exponents, like 2x^2 + 7.

I think I get it!! :D
115/(x-2)-120/x=2/3

115x-120x+240/x(x-2)=2/3

2xsquare-4x=3(115-120x+240)

345x-360x+720-2xsquare+4x

-11x+720-2xsquare

2xsquare+11x-720