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

To calculate the length of the third stage of the train's journey, we use the average speed over the total trip. Summing the known distances of the first two stages and subtracting this from the total distance traveled, which is 700 km, gives us the length of the third stage as 420 km.

Step-by-step explanation:

To find the length of the third stage in a train's journey when the average speed over the entire trip is known, we can use the formula for average speed, which is the total distance traveled divided by the total time taken. According to the given problem, the first two stages took 1 and 2 hours and were 80 km and 200 km long, respectively. Adding the times gives us 3 hours for the first two stages.

The third stage took 4 hours, making the total time for the full journey 7 hours (3 hours + 4 hours). Since the average speed of the train over the course of the trip was 100 km/h, we multiply this by the total time to find the total distance. Thus, the total distance is 700 km (100 km/h * 7 h).

To find the distance covered in the third stage, we subtract the sum of the first two stages (80 km + 200 km) from the total distance. The length of the third stage is 700 km - 280 km = 420 km.

Answer 2

the third stage was 480 km long

Step-by-step 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 =
`(Distance )/(Time)`

Speed =
`(80)/(1)`

Speed 1= 80 km/hr

The speed at stage 2

Speed =
`(Distance )/(Time)`

Speed =
`(200)/(2)`

Speed 2 = 100 km/hr

The speed at stage 3

Speed =
`(Distance )/(Time)`

Speed =
`(x)/(4)`

Speed 3 =
`(x)/(4)`

we kow that average is ,

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

`( 80 + 100+ (x)/(4) )/(3) = 100`

`( 180 + (x)/(4) )/(3) = 100`

`( (720 +x)/(4) )/(3) = 100`

`(720 +x)/(4) * (1)/(3) = 100`

`(720 +x)/(12) = 100`

`720 +x = 100 * 12`

`720 +x = 1200`

`x = 1200- 720`

x = 480