I am having hard time with this maths problem.

Question

Mile who rides a bike is 4 times faster then Kylie who is walking.

If Kylie starts walking 30 minutes before Mile ,

how long will it take Mile on his bike to catch up to Kylie?

Answer 1

r represents Kylie's rate

4r represents Mile's rate

t represents Mile's time

t + 30 represents Kylie's time

 

d = r · t

Miles: d = 4rt

Kylie: d = r(t + 30)

 

For both the distance is equal:

 

4rt = rt + 30r

3rt = 30r

t = 10

 

It take Miles 10 minutes to catch up.

 

Answer 2

Hi Novak,

 

Let Kylie's speed be v. She travels at that constant speed for t₁, and so before Mile begins riding she is a distance d₁ = vt₁ from him.

 

Mile rides his bike at a constant speed 4v, which is 4 times that of Kylie. Let's say that it takes a time T for Mile to catch Kylie. During that time, Kylie continues to walk. So, in time T she is a distance vt₁ + vT from the starting point. During this same time Mile has ridden 4vT. Given that at this time T Mile has caught Kylie, this means that they are at equal distances from their starting point. So, you can equate their distances:

 

4vT = vt₁ + vT

 

Subtract vT from each side.

 

3vT = vt₁

 

We can cancel out v.

 

So, 3T = t₁

 

Or

 

T = t₁/3 = (30 min)/3 = 10 min

 

So, Mile can catch Kylie in 10 min. It is interesting that their speeds don't matter, but only their speed ratio matters.