# Thread: Distance problem with fraction - help to set up equation

1. ## Distance problem with fraction - help to set up equation

Alan and Bob walk from school to the library. Alan takes 40 minutes while Bob takes 20 minutes. If they start walking from the school at the same time, how long will it take for Bob to be 2/5 as far as Alan from the library?

How can I setup an equation for this problem? I'm not quite sure how to deal with the fraction.

2. ## Re: Distance problem with fraction - help to set up equation

Distance = velocity*time
Distance to the library is constant. Let $A,B$ be their respective velocities.

After $t$ minutes, Alan will be a distance of $40A-At$ from the library and Bob will be a distance of $20B-Bt$ from the library. You want that ratio to be 5:2.

$\dfrac{20B-Bt}{40A-At}=\dfrac{2}{5}$
Also $20B=40A$ implies $B=2A$. Plugging in:

$\dfrac{40-2t}{40-t}=\dfrac{2}{5}$
$200-10t=80-2t$

$8t=120$
$t=15$ mins

3. ## Re: Distance problem with fraction - help to set up equation

C'mon Slip...giving full solution is not much "real help"...