A train covers 60 km at a speed of 80 km/h, 100 km at a speed of 90 km/h, and another 140 km at a speed of 120 km/h. Find the average speed for the complete journey. (Round to the nearest integer.)

The correct answer is 99 km/h.

To find the average speed for the complete journey, we use the formula:

$\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}$

Step 1: Calculate the total distance covered.

The train covers three segments of distance:

$\text{Total Distance}=60+100+140=300\text{km}$

Step 2: Calculate the time taken for each segment of the journey.

Using the formula:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

1. Time taken for the first segment ($t_1$):

$t_1=\frac{60}{80}=\frac{3}{4}\text{hours}$

2. Time taken for the second segment ($t_2$):

$t_2=\frac{100}{90}=\frac{10}{9}\text{hours}$

3. Time taken for the third segment ($t_3$):

$t_3=\frac{140}{120}=\frac{7}{6}\text{hours}$

Step 3: Calculate the total time taken for the journey.

$\text{Total Time}=t_1+t_2+t_3$

$\text{Total Time}=\frac{3}{4}+\frac{10}{9}+\frac{7}{6}$

Taking the Least Common Multiple (LCM) of the denominators 4, 9, and 6, which is 36:

$\text{Total Time}=\frac{27+40+42}{36}=\frac{109}{36}\text{hours}$

Step 4: Calculate the average speed.

$\text{Average Speed}=\frac{300}{109/36}=\frac{300\times 36}{109}=\frac{10800}{109}$

$\text{Average Speed}\approx 99.08\text{km/h}$

Rounding to the nearest integer, the average speed for the complete journey is 99 km/h.