Find time when particular distance between two people achieved

Suppose A travels at 16 kmph. B travels at 10 kmph. Both start at same time in same direction. After how much time will they have a distance of 3 kms between them?

• Is this all the information given? Are they traveling in opposite directions? Commented Jul 13, 2017 at 15:30
• @D.Beec This is all the information given. And they travel in same direction. What more information is required to solve this? Commented Jul 13, 2017 at 15:31
• What direction they travel in relative to each other is required to answer this question, and I didn't see you mention it in the problem Commented Jul 13, 2017 at 15:32
• @D.Beec Ok, I've now mentioned it in the problem Commented Jul 13, 2017 at 15:33
• Unstated in the problem is whether or not they start from the same place.
– amd
Commented Jul 13, 2017 at 20:34

Hint: How fast does the distance between them grow?

• 6 kmph ? ........ Commented Jul 13, 2017 at 15:33
• That is correct. So if they want to be 3 km apart, how long does that take? Commented Jul 13, 2017 at 15:34
• ;-P 30mins? .... Commented Jul 13, 2017 at 15:34

Since for uniform motion, $s=vt$, here $v_1t-v_2t=s_1-s_2=s$, or $16t-10t=3$. So $6t=3$, and $t=.5 hours$

@Ross Millikan has the perfect answer (+1). That is the way I'd solve it in the real world. However, this question sounds like homework. If it is, then your teacher will want to see your logic (that is, the equation you use) to prove you can solve any problem of this type.

First, choose a variable. I like to use $t$ for time problems. Since the people travel in km/h, we will let $t$ have hours as units. Since person A travels at 16 km/h, when $t=1$, the distance traveled is 16 km. Simple, right?

The problem asks for the distance between the two. In an equation, this means subtraction. An expression that would express the distance between the two people is $$16t-10t$$ where $t$ is in hours. For example, after $3$ hours, the distance between them is $16\cdot3-10\cdot3=48-30=18 \text{km}$.

The problem asks for how much time has elapsed when the two people are $3$ km apart. So we make an equation out of the expression: we set the expression equal to 3. $$16t-10t=3$$

Now solve for $t$. You should get $t=\frac{1}{2}$ hour, which is $30$ minutes.