Question

When they are both racing on hoverboards, Victoria is 3 times as fast as her brother Max. When she is on foot, she is 3 times slower than Max on his hoverboard. They took off on hoverboards at the same time, but after 12 minutes, Victoria’s hoverboard broke and she immediately started to run. If the race was a tie, how long, in minutes, did it last from start to finish?

Answer 1

We know that ; Distance = Speed × Time

So, let the speed of Max be = s

Time taken = t minutes

So, at 12 minutes,

Max covers a distance of =
`12* s=12s`

As given, Victoria is 3 times as fast as her brother Max.

So, distance covered by Victoria will be =
`12* s*3=36s`

After 12 minutes,

Victoria’s hover board broke and she immediately started to run.

Given is when Victoria is on foot, she is 3 times slower than Max on his hover board.

Distance covered by Max =
`s*(t-12)=(t-12)s`

And distance covered by Victoria =
`(s)/(3) *(t-12)`

As given, if the race was a tie:

Total distance of Max = Total distance of Victoria

`12s+(t-12)s=36s+(s(t-12))/(3)`

Solving this we get,

`3t=96+t`

`2t=96`

Hence, t=48

So, it lasted from start to finish is 48 minutes.