Question

El recorrido de una etapa de una vuelta ciclística tiene una longitud de 213 kilometros y un ciclista recorre 2/3 del trayecto en 5 horas

Answer 1

the question in English

The route of a stage of a cycle tour is 213 km long and a cyclist covers 2/3 of the route in five hours.

a) How many kilometers are left to finish the stage?

b) If he continues with the same average speed, how much time does he have left to finish the stage?

Step 1

we know that

1) Total kilometers of a stage is $213\ km$

2) The cyclist covers $\frac{2}{3}$ of the route

so

the kilometers remaining to finish the stage is equal to

$(1-\frac{2}{3})*213= \frac{1}{3}*213\\ \\=71\ km$

therefore

the answer   Part a) is

$71\ km$

Step 2

Find the average speed of the cyclist

we know that

the speed is equal to

$speed=\frac{distance}{time}$

we have

$time=5\ hours\\ distance=\frac{2}{3}*213=142\ km$

substitute

$speed=\frac{142}{5}=28.4\frac{km}{h}$

Step 3

Find the time remaining to finish the stage

we know that

$speed=\frac{distance}{time}$

Solve for the time

$time=\frac{distance}{speed}$

we have

$distance=71\ km\\ speed=28.4\frac{km}{h}$

substitute

$time=\frac{71}{28.4}=2.5\ hours$

therefore

the answer Part b) is

$2.5\ hours$