# Need Help with Brain Boot Camp problem

#### Kristin H 0309

##### New member
" A car and a motorcycle set off from the same point to travel the same journey. The car sets off two minutes before the motorcycle. If the car travels at 60km/hr and the motorcycle travels at 80km/hr how many kilometers from the starting point will they draw level? "
Thank you so much for your help! It has been many, many years since I learned Algebra in school!

#### Subhotosh Khan

##### Super Moderator
Staff member
" A car and a motorcycle set off from the same point to travel the same journey. The car sets off two minutes before the motorcycle. If the car travels at 60km/hr and the motorcycle travels at 80km/hr how many kilometers from the starting point will they draw level? "
Thank you so much for your help! It has been many, many years since I learned Algebra in school!

Please share your work/thoughts and context of the problem (what is the subject topic?) - so that we know where to begin to help you.

Hint: The "find" of the problem is:

"how many kilometers from the starting point will they draw level?"

Assume:

The distance to draw level = d km

How long the car will take to travel this distance = d/60 hr

How long the MC will take to travel this distance = d/80 hr

Continue.....

#### Kristin H 0309

##### New member
I'm still very frustrated by this problem but will make a stab at the solution:
d/.75 + 2/1 = d/1
1.5= 2d
3=d

#### Romsek

##### Full Member
$$\displaystyle \text{Supposing the car starts at time t=0~hr, it's distance from start will be d_c(t) = 60t~km}$$

$$\displaystyle \text{Similarly the motorcycle distance is given by d_m(t) = 80\left(t-\dfrac{2}{60}\right)~km}$$

$$\displaystyle \text{We want to find out the time these two distances are equal}\\ 60t=80\left(t - \dfrac{1}{30}\right) = 80t - \dfrac 8 3\\ \dfrac 8 3 = 20 t\\ t = \dfrac{8}{60} = \dfrac{2}{15}~hr\\ d_c(t) = d_m(t) = 60 \dfrac{2}{15} = 8~km$$

#### Subhotosh Khan

##### Super Moderator
Staff member
I'm still very frustrated by this problem but will make a stab at the solution:
d/.75 + 2/1 = d/1
1.5= 2d
3=d
How did you get those equations?

Those are so misguided that those are NOT EVEN WRONG!

I'll do this problem for you but I am afraid you are not ready for these types of problems.

" A car and a motorcycle set off from the same point to travel the same journey. The car sets off two minutes before the motorcycle. If the car travels at 60km/hr and the motorcycle travels at 80km/hr how many kilometers from the starting point will they draw level? "

One important thing to note in this problem is to note that car spends more time on road than the motorcycle.

How much longer (in time) did the car spend on the road? = 2 minutes = 1/30 hours

Then

d/60 = d/80 + 1/30

d/60 - d/80 = 1/30

$$\displaystyle \dfrac{4*d - 3*d}{240} \ = \dfrac{1}{30}$$

d = 240/30 = 8 km