Question

The three stages of a train route took 1 hour ,2 hours ,and 4 hours . The first two stages were 80km and 200km of the train average speed over the course of the trip was 100km/h how many kilometers long was the third stage

Answer 1

Answer:

the third stage was 480 km long

Explanation:

Stage 1:

Time = 1 hours

Speed = 80km

Stage 2:

Time =  2 hours

Speed = 200km

Stage 3:

Time =  4 hours

Let the Distance at the stage 3 be x

Average speed of the train route = 100 km/h

So

$\frac{ \text{speed at stage 1} + \text{speed at stage 2} + \text{speed at stage 3}}{3} = 0$

$\frac{ \text{speed at stage 1} + \text{speed at stage 2} + \text{speed at stage 3}}{3} = 100$

Lets find the speed at stage 1

Speed =  $\frac{Distance }{Time}$

Speed =  $\frac{80}{1}$

Speed 1= 80 km/hr

The speed at stage 2

Speed =  $\frac{Distance }{Time}$

Speed =  $\frac{200}{2}$

Speed 2  = 100 km/hr

The speed at stage 3

Speed =  $\frac{Distance }{Time}$

Speed =  $\frac{x}{4}$

Speed 3  = $\frac{x}{4}$

we kow that average is ,

$\frac{ \text{speed 1} + \text{speed 2} + \text{speed 3}}{3} = 100$

$\frac{ 80 + 100+ \frac{x}{4} }{3} = 100$

$\frac{ 180 + \frac{x}{4} }{3} = 100$

$\frac{ \frac{720 +x}{4} }{3} = 100$

$\frac{720 +x}{4} \times \frac{1}{3} = 100$

$\frac{720 +x}{12} = 100$

$720 +x = 100 \times 12$

$720 +x = 1200$

$x = 1200- 720$

x = 480