# Thread: A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x etc.

1. ## A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x etc.

Hello! I would like some help with this task.

A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x. Find the time taken when his speed is reduced by 2 km/h. If the difference between the times is 1 hour, find the orginal speed, x km/h.

Thank you!

2. Originally Posted by Anna55
Hello! I would like some help with this task.

A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x. Find the time taken when his speed is reduced by 2 km/h. If the difference between the times is 1 hour, find the orginal speed, x km/h.

Thank you!
Hi Anna55,

Using $rt=D$, we first have:

$xt=40$

$t=\dfrac{40}{x}$

After decreasing the rate by 2 km/h, we have:

$(x-2)t=40$

$t=\dfrac{40}{x-2}$

The difference in time is 1 hour. So...

$\dfrac{40}{x-2}-\dfrac{40}{x}=1$

Can you finish up?

3. Thank you. I understand everything except why you are doing this (x+2)t=40 when is speed are reduced by 2km/h.

4. Originally Posted by Anna55
Thank you. I understand everything except why you are doing this (x+2)t=40 when is speed are reduced by 2km/h.
I misread your problem. Just change the + to a -. And reverse the order of the subtraction. Sorry! I'll edit my post so you can see.

5. Thank you! I tried to solve the equation, however I cannot. First I extended the denominator so every fraction hade the same denominator (x-2) x. After that I moved over 1 to the left side so everything equaled 0. After that I cannot continue. Can you please show me.

6. Originally Posted by Anna55
Thank you! I tried to solve the equation, however I cannot. First I extended the denominator so every fraction hade the same denominator (x-2) x. After that I moved over 1 to the left side so everything equaled 0. After that I cannot continue. Can you please show me.
Hi Anna55,

Sorry for the confusion initially. Here is the complete solution.

$\dfrac{40}{x-2}-\dfrac{40}{x}=1$

Multiply each side by $x(x-2)$

$40x-40(x-2)=x(x-2)$

$40-40x+80=x^2-2x$

$x^2-2x-80=0$

$(x-10)(x+8)=0$

$\boxed{x=10}$

Disregard the negative solution.

7. Thank you very much masters! I understand everything now.

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