Question

Vicente and Carla each ran 8 laps around a track. They started at the same time and place. If Vicente ran 1.5 times as fast as Carla, how many laps did Carla have left to finish when Vicente finished his 8th lap?

1. Philomena
The distance left in 8 laps for Carla when Vicente has already finished his 8th lap is 2 2/3 laps.

### What is speed?

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
Speed = Distance Covered / Time taken
Let the distance of a single lap be x units. Also, the time it takes for Carla to complete a single round is represented by y.
Speed of Carla = x/t
Speed of Vicente = 1.5(x/t)
Now, the time it will take Vincente to complete the 8 laps is,
Time = 8x / [1.5(x/t)]
Time = 8tx / 1.5x
Time = 16t/3
Distance covered by Carla by the time Vincente completed 8 laps,
Distance = Speed × Time
= (x/t) × (16t/3)
= 16x / 3
Now, the distance left in 8 laps is,
Distance left in 8 laps = Total distance – Distance covered
= 8x – (16x/3)
= (24x – 16x)/3
= 8x / 3
= 2 2/3 x
= 2 2/3 laps
Hence, the distance left in 8 laps for Carla when Vicente has already finished his 8th lap is 2 2/3 laps.