Stuck on a basic thinking question

Question

Stewart and Michael have arranged to meet. Michael is about to set off on his bicycle, and at the same time Stewart is going to run to meet him. Michael can cycle at a steady 20 kilometres per hour and Stewart can run at a steady 12 kilometres per hour. They live 8 kilometres from each other. How long will it be before they meet?

I have drawn out the situation but still am confused. This is from a thinking skills assessment so I don't think much mathematics is required.

Can I have a miniscule hint?

Thanks

Answer 1

If they go directly, they need to travel a total of $8$km. Thus $$8 \text{km} = 20 \frac{\text{km}}{\text h} \cdot t + 12 \frac{\text{km}}{\text h} \cdot t = 32 \frac{\text{km}}{\text h} \cdot t$$ That makes $15$ minutes.

Answer 2

They are nearing each other at the combined speed of 32 km/h...

Answer 3

Let $m$ be Michael's speed in $km/h$ and $s$ be Stewart's speed in $km/h$. They are traveling towards each other, so their speeds combine in an additive way. Taking $t$ as the time in hours, we have $t\cdot m+t\cdot s=8.$ Can you take it from here?

Answer 4

Let they meet at point C. Micheal will take x/20 hr to reach C and Stewart will take (8-x)/12 hr to reach C. Both started together and reached together on C, so, $\frac{x}{20}=\frac{8-x}{12}$ , which gives x=5, that means they will meet at 5 km from point A. S0 they will meet after 1/4 hr OR 15 minutes.