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

The answer is 48 minutes.

Explanation:

Let the speed of Max on hoverboard be = x

Then the speed of Victoria on hoverboard will be = 3x

Now its given that the speed of Victoria on foot is 1/3 of the speed of Max on hoverboard, this is = x/3

Formula of speed =
`(distance)/(time)`

Let the time taken by both to complete the race be t minutes.

Hence, distance covered by Victoria in 12 minutes + distance covered by Victoria on foot = distance covered by Max on hoverboard. Now in equation form this becomes:

`36x+(xt)/(3)-4x=xt`

Simplifying this we get,

`36+(t)/(3)-4=t`

`(2t)/(3)=32`

This gives t=48

Hence, t = 48 minutes.

Answer 2

The time taken from start to finish is 48 minutes.

Explanation:

Given : 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.

To find : How long, in minutes, did it last from start to finish?

Solution :

Distance = Speed × Time

Let the speed of Max = s

Time taken = t

At 12 minutes,

Distance covered by Max =
`s*12=12s`

Victoria is 3 times as fast as her brother Max.

Distance covered by Victoria =
`3* s*12=36s`

After 12 minutes,

Victoria’s hoverboard broke and she immediately started to run.

When Victoria is on foot, she is 3 times slower than Max on his hoverboard.

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

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

Since the race was a tie, then

Total distance of Max = Total distance of Victoria

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

`s(12+(t-12))=(s(96+t))/(3)`

`t=(96+t)/(3)`

`3t=96+t`

`2t=96`

`t=48`

The time taken from start to finish is 48 minutes.