Logical reasoning question

Practice Question Solving
1

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 20km/h and Stewart can run at a steady 12km/h.
They live 8km from each other.
How long will it be before they meet?

Hi everyone,

The answer for this question is 15 minutes.
I tried solving when t1=t2 so d1/v1=d2/v2 but i’m stuck in my calculation.
How can this question be solved?

Thanks!!

2

We can define our variables as:

  • d: distance between Michael and Stewart
  • v_1: velocity of Michael (in km/h)
  • v_2: velocity of Stewart (in km/h)
  • t: time taken to meet (in hours)

Using the formula distance = rate x time, we can find the distance traveled by Michael and Stewart as:

d_1 = v_1t = 20t

d_2 = v_2t = 12t

Since they are moving towards each other, their combined distance traveled will be equal to the distance between them, which is d = 8 km. Therefore, we have the equation:

d_1 + d_2 = 8

Substituting the expressions we found earlier for d_1 and d_2, we get:

20t + 12t = 8

Simplifying this equation, we can get t on one side of the equation:

32t = 8

t = \frac{8}{32} = 0.25 hours.

To convert this time to minutes, we can multiply it by 60:

t = 0.25 \text{ hours} \times 60 \text{ minutes/hour} = 15 \text{ minutes}.

Therefore, it will take Michael and Stewart \boxed{15 \text{ minutes}} to meet.

I hope this helps! Let me know if you have any questions.

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